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Theory of capacities
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</div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:20px;margin-bottom:30px"> <ul class="nav nav-tabs article-tab"> <li class="nav-item active"> <a class="nav-link active" lang="fr" data-bs-toggle="tab" data-bs-target="#abstract-fr" href="#abstract-fr"><span title='Fran莽ais '>R茅sum茅</span></a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div lang="fr" id="abstract-fr" class="tab-pane fade show active"> <p>C鈥檈st un essai de th茅orie g茅n茅rale des fonctions croissantes d鈥檈nsemble. On est amen茅 脿 mettre en 茅vidence diverses classes importantes de telles fonctions, en particulier la classe des fonctions fortement sous-additives, pour lesquelles existe une th茅orie analogue 脿 celle de la mesure, et une sous-classe de celle-ci, 脿 savoir la classe des fonctions altern茅es d鈥檕rdre infini, analogues aux fonctions num茅riques compl猫tement monotones.</p><p>La capacit茅 classique est une telle fonction d鈥檈nsemble聽; il en r茅sulte l鈥檌dentit茅 des capacit茅s int茅rieure et ext茅rieure de tout ensemble bor茅lien ou analytique.</p><p>Un outil de recherche puissant est la repr茅sentation int茅grale des fonctions d鈥檜ne classe additive et convexe au moyen des 茅l茅ments extr茅maux d鈥檜ne telle classe. Cette repr茅sentation permet d鈥檌dentifier les fonctions altern茅es d鈥檕rdre infini avec certaines probabilit茅s associ茅es 脿 l鈥檈nsemble variable.</p> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:10px;margin-bottom:10px"> <ul class="nav nav-tabs article-tab"> <li class="nav-item"><a class="nav-link active" data-bs-toggle="tab" data-bs-target="#info-tab" href="#info-tab">D茅tail</a></li> <li class="nav-item"><a class="nav-link" data-bs-toggle="tab"data-bs-target="#citation-tab" href="#citation-tab">Export</a></li> <li class="nav-item"> <a class="nav-link " data-bs-toggle="tab" data-toggle="tab" data-bs-target="#how-to-cite-tab" href="#how-to-cite-tab">Comment citer</a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div id="info-tab" class="tab-pane fade show active"> <!--Mis en ligne le : <time datetime="2024-03-10">2024-03-10</time><br>--> <div style="margin-top:5px"> <a href="https://eudml.org/doc/73714" class="badge bg-secondary rounded-pill ref-badge extid-badge"> EuDML </a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=18,295g" class="badge bg-secondary rounded-pill ref-badge extid-badge"> MR </a> <a href="https://zbmath.org/?q=an:0064.35101" class="badge bg-secondary rounded-pill ref-badge extid-badge"> Zbl </a> </div> DOI : <a href="https://doi.org/10.5802/aif.53">10.5802/aif.53</a> <br> <div style="margin-top:5px"> </div> <div style="margin-top:5px"> </div> </div> <div id="citation-tab" class="tab-pane fade"> <div class="upper"> <ul class="nav nav-pills"> <li role="presentation" class="nav-item"><a class="nav-link active" data-bs-toggle="tab" data-bs-target="#bibtex" href="#bibtex">BibTeX</a></li> <li role="presentation" class="nav-item"><a class="nav-link" data-bs-toggle="tab" data-bs-target="#ris" href="#ris">RIS</a></li> <li role="presentation" class="nav-item"><a class="nav-link" data-bs-toggle="tab" data-bs-target="#enw" href="#enw">EndNote</a></li> </ul> <div class="tab-content"> <div id="bibtex" class="tab-pane fade show active"> <pre class="upper-right-content" id="bibtex-div">@article{AIF_1954__5__131_0, author = {Choquet, Gustave}, title = {Theory of capacities}, journal = {Annales de l'Institut Fourier}, pages = {131--295}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {5}, year = {1954}, doi = {10.5802/aif.53}, zbl = {0064.35101}, mrnumber = {18,295g}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.53/} }</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#bibtex-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="T茅l茅charger" href="/export_citation/AIF_1954__5__131_0/bib/"></a> </div> <div id="ris" class="tab-pane fade"> <pre class="upper-right-content" id="ris-div">TY - JOUR AU - Choquet, Gustave TI - Theory of capacities JO - Annales de l'Institut Fourier PY - 1954 SP - 131 EP - 295 VL - 5 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.53/ DO - 10.5802/aif.53 LA - en ID - AIF_1954__5__131_0 ER - </pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#ris-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="T茅l茅charger" href="/export_citation/AIF_1954__5__131_0/ris/"></a> </div> <div id="enw" class="tab-pane fade"> <pre class="upper-right-content" id="enw-div">%0 Journal Article %A Choquet, Gustave %T Theory of capacities %J Annales de l'Institut Fourier %D 1954 %P 131-295 %V 5 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.53/ %R 10.5802/aif.53 %G en %F AIF_1954__5__131_0</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#enw-div" aria-hidden="true" title="Copier dans le presse-papier"></button> <a class="fa fa-download export-button btn btn-primary" title="T茅l茅charger" href="/export_citation/AIF_1954__5__131_0/enw/"></a> </div> </div> </div> </div> <div id="how-to-cite-tab" class="tab-pane fade "> <div class="upper-right"> <pre class="upper-right-content" id="how-to-cite-div">Choquet, Gustave. Theory of capacities. Annales de l'Institut Fourier, Tome 5 (1954), pp. 131-295. doi : 10.5802/aif.53. https://aif.centre-mersenne.org/articles/10.5802/aif.53/</pre> <button class="fa fa-clipboard copy-button btn btn-primary" data-clipboard-action="copy" data-clipboard-target="#how-to-cite-div" aria-hidden="true" title="Copier dans le presse-papier"></button> </div> </div> </div> </div> </div> </div> <div> <div class="col-12"> <div style="margin-top:30px;margin-bottom:10px"> <ul class="nav nav-tabs article-tab" > <li class="nav-item" id="main-citations-li" > <a class="nav-link active" data-bs-toggle="tab" data-bs-target="#references-tab" href="#references-tab">Bibliographie</a> </li> <li class="nav-item" id="citations-html" style="display:none"> <a class="nav-link" data-bs-toggle="tab" data-bs-target="#citations-tab" href="#citations-tab">Cit茅 par</a> </li> </ul> <div class="tab-content" style="margin-top:10px"> <div id="references-tab" class="tab-pane fade show active"> <div style="margin-top:11px;margin-bottom: 0px"> <p class="bibitemcls " > [1] <span class="citation-author">Aissen, Michael</span>. <span class="citation-document-title">A class of super-additive functions</span>. 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