V: 07, 77-81, LNM 191 (1971)
DELLACHERIE, Claude
Quelques commentaires sur les prolongements de capacités (
Descriptive set theory)
Remarks on the extension of capacities from sets to functions. Probably superseded by the work of Mokobodzki on functional capacities
Comment: See Dellacherie-Meyer,
Probabilités et Potentiel, Chap. XI: capacités fonctionnelles
Keywords: CapacitiesNature: Original
Retrieve article from Numdam
V: 08, 82-85, LNM 191 (1971)
DELLACHERIE, Claude
Une démonstration du théorème de séparation des ensembles analytiques (
Descriptive set theory)
The first separation theorem can be deduced from Choquet's capacity theorem
Comment: Starting point in Sion,
Ann. Inst. Fourier, 13, 1963. This proof has become standard, see Dellacherie-Meyer,
Probabilités et Potentiel, Chap. III
Keywords: Analytic sets,
Capacities,
Separation theoremNature: Original Retrieve article from Numdam
V: 11, 103-126, LNM 191 (1971)
DELLACHERIE, Claude
Ensembles pavés et rabotages (
Descriptive set theory)
A systematic study of the ``rabotages de Sierpinski'', used in Dellacherie
306 to solve several problems in probabilistic potential theory. The main paper on this subject
Comment: See Dellacherie,
Capacités et Processus Stochastiques, 1970. Author should be consulted on recent developments (see
1526)
Keywords: Analytic sets,
Capacities,
Sierpinski's ``rabotages''Nature: Original Retrieve article from Numdam
X: 32, 579-593, LNM 511 (1976)
DELLACHERIE, Claude
Compléments aux exposés sur les ensembles analytiques (
Descriptive set theory)
A new proof of Novikov's theorem (see
1028 and the corresponding comments) is given in the form of a Choquet theorem for multicapacities (with infinitely many arguments). Another (unrelated) result is a complement to
919 and
920, which study the space of stopping times. The language of stopping times is used to prove a deep section theorem due to Kondo
Keywords: Analytic sets,
Section theorems,
CapacitiesNature: Original Retrieve article from Numdam
XII: 36, 489-490, LNM 649 (1978)
MOKOBODZKI, Gabriel
Domination d'une mesure par une capacité (
Measure theory)
A bounded measure $\mu$ is said to be dominated by a capacity $C$ (countably subadditive, continuous along increasing sequences; neither strong subadditivity nor decreasing sequences are mentioned) if all sets of capacity $0$ have also measure $0$. The main result then states that the space can be decomposed into a set $A_0$ of capacity $0$, and disjoint sets $A_n$ on each of which $\mu$ is smaller than a multiple of $C$
Keywords: Radon-Nikodym theorem,
CapacitiesNature: Original Retrieve article from Numdam
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 PotentielKeywords: Capacities,
Analytic setsNature: Original Retrieve article from Numdam
XV: 26, 351-370, LNM 850 (1981)
DELLACHERIE, Claude
Mesurabilité des débuts et théorème de section~: le lot à la portée de toutes les bourses (
General theory of processes)
One of the main topics in these seminars has been the application to stochastic processes of results from descriptive set theory and capacity theory, at different levels. Since these results are considered difficult, many attempts have been made to shorten and simplify the exposition. A noteworthy one was
511, in which Dellacherie introduced ``rabotages'' (
306) to develop the theory without analytic sets; see also
1246,
1255. The main feature of this paper is a new interpretation of rabotages as a two-persons game, ascribed to Telgarsky though no reference is given, leading to a pleasant exposition of the whole theory and its main applications
Keywords: Section theorems,
Capacities,
Sierpinski's ``rabotages''Nature: Original Retrieve article from Numdam
