Accueil /Equivalence de vocabulaire en théorie de la mesure ensembliste

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  • Deprecated function: Return type of DatabaseStatementBase::execute($args = [], $options = []) should either be compatible with PDOStatement::execute(?array $params = null): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2244 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_random_bytes() (line 2268 of /home/laurentp/www/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $type declared before required parameter $key is implicitly treated as a required parameter in include_once() (line 1389 of /home/laurentp/www/includes/bootstrap.inc).
  • Deprecated function: Return type of DateObject::__wakeup() should either be compatible with DateTime::__wakeup(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
  • Deprecated function: Return type of DateObject::format($format, $force = false) should either be compatible with DateTime::format(string $format): string, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
  • Deprecated function: Return type of DateObject::setTimezone($tz, $force = false) should either be compatible with DateTime::setTimezone(DateTimeZone $timezone): DateTime, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
  • Deprecated function: Optional parameter $input declared before required parameter $form_state is implicitly treated as a required parameter in include_once() (line 1389 of /home/laurentp/www/includes/bootstrap.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : rtrim(): Passing null to parameter #1 ($string) of type string is deprecated dans url() (ligne 2349 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property PDOException::$query_string is deprecated dans DatabaseConnection->query() (ligne 770 dans /home/laurentp/www/includes/database/database.inc).
  • Deprecated function : Creation of dynamic property PDOException::$args is deprecated dans DatabaseConnection->query() (ligne 772 dans /home/laurentp/www/includes/database/database.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated dans url_is_external() (ligne 2393 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated dans url_is_external() (ligne 2395 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : ltrim(): Passing null to parameter #1 ($string) of type string is deprecated dans url() (ligne 2311 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).

Equivalence de vocabulaire en théorie de la mesure ensembliste

Soumis par Laurent Petit cours le mar, 11/09/2012 - 07:24

Les noms apparaissant en théorie de la mesure ensembliste ne sont pas toujours les même notamment entre les textes anglais et français, ceci permettra également de rappeler certaines définitions:

Notations: Ω désignera un ensemble, P(Ω) l'ensemble des parties de Ω.

Définition: Pré-clan ou demi-clan ou semi-anneau de sous-ensembles de Ω (semi-ring of subsets) A ⊂ P(Ω) :
1) Ø ∈ A
2) A est stable par intersection finie
3) Pour tout élément E et F de A tel que E ⊂ F, E\F est union finie disjointe d'éléments de A deux à deux disjoints

Définition: Pré clan unifère ou semi-algèbre de Boole (semi algebra): un pré-clan qui contient Ω

Définition: Clan unifère ou algèbre de sous-ensemble (algebra of subsets) : une famille de sous ensemble de Ω contenant Ω, stable par union finie et stable par complémentaire. Il est équivalent à la stabilité par union finie d'exiger la stabilité par intersection finie.

Uncaught exception thrown in session handler.

PDOException: SQLSTATE[42000]: Syntax error or access violation: 1142 INSERT command denied to user 'laurentpabcm'@'10.2.20.88' for table 'drupclonesessions': INSERT INTO {sessions} (sid, ssid, uid, cache, hostname, session, timestamp) VALUES (:db_insert_placeholder_0, :db_insert_placeholder_1, :db_insert_placeholder_2, :db_insert_placeholder_3, :db_insert_placeholder_4, :db_insert_placeholder_5, :db_insert_placeholder_6); Array ( [:db_insert_placeholder_0] => sFmxfsSC1d9Hq-wDcy0o8Az0x4r3TNa-nHUmhGTiyMw [:db_insert_placeholder_1] => sFmxfsSC1d9Hq-wDcy0o8Az0x4r3TNa-nHUmhGTiyMw [:db_insert_placeholder_2] => 0 [:db_insert_placeholder_3] => 0 [:db_insert_placeholder_4] => 18.207.133.13 [:db_insert_placeholder_5] => messages|a:1:{s:5:"error";a:6:{i:0;s:300:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property SelectQuery::$alterTags is deprecated dans <em class="placeholder">SelectQuery->addTag()</em> (ligne <em class="placeholder">978</em> dans <em class="placeholder">/home/laurentp/www/includes/database/select.inc</em>).";i:1;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";i:2;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";i:3;s:300:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property SelectQuery::$alterTags is deprecated dans <em class="placeholder">SelectQuery->addTag()</em> (ligne <em class="placeholder">978</em> dans <em class="placeholder">/home/laurentp/www/includes/database/select.inc</em>).";i:4;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";i:5;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";}} [:db_insert_placeholder_6] => 1725871732 ) in _drupal_session_write() (line 209 of /home/laurentp/www/includes/session.inc).