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XII: 46, 707-738, LNM 649 (1978)

**DELLACHERIE, Claude**

Théorie unifiée des capacités et des ensembles analytiques (Descriptive set theory)

A Choquet capacity takes one set as argument and produces a number. Along the years, one has considered multicapacities (which take as arguments finitely many sets) and capacitary operators (which produce sets instead of numbers). The essential result of this paper is that, if one allows functions of infinitely many arguments which produce sets, then the corresponding ``Choquet theorem'' gives all the classical results at a time, without need of an independent theory of analytic sets

Comment: For a more systematic exposition, see Chapter XI of Dellacherie-Meyer*Probabilités et Potentiel*

Keywords: Capacities, Analytic sets

Nature: Original

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Théorie unifiée des capacités et des ensembles analytiques (Descriptive set theory)

A Choquet capacity takes one set as argument and produces a number. Along the years, one has considered multicapacities (which take as arguments finitely many sets) and capacitary operators (which produce sets instead of numbers). The essential result of this paper is that, if one allows functions of infinitely many arguments which produce sets, then the corresponding ``Choquet theorem'' gives all the classical results at a time, without need of an independent theory of analytic sets

Comment: For a more systematic exposition, see Chapter XI of Dellacherie-Meyer

Keywords: Capacities, Analytic sets

Nature: Original

Retrieve article from Numdam