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III: 06, 115-136, LNM 88 (1969)

**DELLACHERIE, Claude**

Ensembles aléatoires II (Descriptive set theory, Markov processes)

Among the many proofs that an uncountable Borel set of the line contains a perfect set, a proof of Sierpinski (*Fund. Math.*, **5**, 1924) can be extended to an abstract set-up to show that a non-semi-polar Borel set contains a non-semi-polar compact set

Comment: See Dellacherie,*Capacités et Processus Stochastiques,* Springer 1972. More recent proofs no longer depend on ``rabotages'': Dellacherie-Meyer, *Probabilités et potentiel,* Appendix to Chapter IV

Keywords: Sierpinski's ``rabotages'', Semi-polar sets

Nature: Original

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IV: 06, 71-72, LNM 124 (1970)

**DELLACHERIE, Claude**

Au sujet des sauts d'un processus de Hunt (Markov processes)

Two a.s. results on jumps: the process cannot jump*from * a semi-polar set; at the first hitting time of any finely closed set $F$, either the process does not jump, or it jumps from outside $F$

Comment: Both results are improvements of previous results of Meyer and Weil

Keywords: Hunt processes, Semi-polar sets

Nature: Original

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V: 06, 76-76, LNM 191 (1971)

**CHUNG, Kai Lai**

A simple proof of Doob's convergence theorem (Potential theory)

Doob's theorem is a version of the main convergence theorem of potential theory: the limit of a decreasing sequence of excessive functions differs of its regularized version on a semi-polar set

Comment: It is also shown that a function $f$ satisfying $f\ge P_Kf$ for all compact sets $K$ differs from its regularized function on a semi-polar set

Keywords: Excessive functions, Semi-polar sets

Nature: New exposition of known results

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V: 26, 275-277, LNM 191 (1971)

**REVUZ, Daniel**

Remarque sur les potentiels de mesure (Markov processes, Potential theory)

The standard proof of the equivalence between semi-polar sets being polar and a very precise domination principle (Blumenthal-Getoor,*Markov Processes and Potential Theory,* 1968) uses the assumption that excessive functions are lower semicontinuous. This assumption is weakened

Comment: To be asked

Keywords: Polar sets, Semi-polar sets, Excessive functions

Nature: Original

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VII: 07, 51-57, LNM 321 (1973)

**DELLACHERIE, Claude**

Une conjecture sur les ensembles semi-polaires (Markov processes)

For a right process satisfying the absolute continuity hypothesis and assuming singletons are semi-polar sets, it is conjectured that a (nearly-)Borel set is semipolar if and only if it does not contain uncountable families of disjoint, non-polar compact sets. This statement implies that two processes which have the same polar sets also have the same semi-polar sets

Comment: The conjecture can be proved, using a general result of Mokobodzki, see 1238

Keywords: Polar sets, Semi-polar sets

Nature: Original

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IX: 29, 495-495, LNM 465 (1975)

**DELLACHERIE, Claude**

Une propriété des ensembles semi-polaires (Markov processes)

It is shown that semi-polar sets are exactly those which have potential 0 for all continuous additive functionals (or for all time-changed processes)

Keywords: Semi-polar sets

Nature: Original

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X: 29, 544-544, LNM 511 (1976)

**DELLACHERIE, Claude**

Correction à des exposés de 1973/74 (Descriptive set theory)

Corrections to 915 and 918

Keywords: Analytic sets, Semi-polar sets, Suslin spaces

Nature: Original

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XII: 38, 509-511, LNM 649 (1978)

**DELLACHERIE, Claude**

Appendice à l'exposé de Mokobodzki (Measure theory, General theory of processes)

Some comments on 1237: a historical remark, a relation with a result of Talagrand, the inclusion of a converse (due to Horowitz) to the case of finite sections, and the solution to the conjecture from 707

Keywords: Sets with countable sections, Semi-polar sets

Nature: Original

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XII: 43, 564-566, LNM 649 (1978)

**DELLACHERIE, Claude**; **MOKOBODZKI, Gabriel**

Deux propriétés des ensembles minces (abstraits) (Descriptive set theory)

Given a class ${\cal S}$ of Borel sets understood as ``small'' sets, the class ${\cal L}$ consisting of their conplements understood as ``large'' sets, a set $A$ is said to be ${\cal S}$-thin if does not contain uncountably many disjoint ``large'' sets. For instance, if ${\cal S}$ is the class of polar sets, then thin sets are the same as semi-polar sets. Two general theorems are proved here on thin sets

Keywords: Thin sets, Semi-polar sets, Essential suprema

Nature: Original

Retrieve article from Numdam

Ensembles aléatoires II (Descriptive set theory, Markov processes)

Among the many proofs that an uncountable Borel set of the line contains a perfect set, a proof of Sierpinski (

Comment: See Dellacherie,

Keywords: Sierpinski's ``rabotages'', Semi-polar sets

Nature: Original

Retrieve article from Numdam

IV: 06, 71-72, LNM 124 (1970)

Au sujet des sauts d'un processus de Hunt (Markov processes)

Two a.s. results on jumps: the process cannot jump

Comment: Both results are improvements of previous results of Meyer and Weil

Keywords: Hunt processes, Semi-polar sets

Nature: Original

Retrieve article from Numdam

V: 06, 76-76, LNM 191 (1971)

A simple proof of Doob's convergence theorem (Potential theory)

Doob's theorem is a version of the main convergence theorem of potential theory: the limit of a decreasing sequence of excessive functions differs of its regularized version on a semi-polar set

Comment: It is also shown that a function $f$ satisfying $f\ge P_Kf$ for all compact sets $K$ differs from its regularized function on a semi-polar set

Keywords: Excessive functions, Semi-polar sets

Nature: New exposition of known results

Retrieve article from Numdam

V: 26, 275-277, LNM 191 (1971)

Remarque sur les potentiels de mesure (Markov processes, Potential theory)

The standard proof of the equivalence between semi-polar sets being polar and a very precise domination principle (Blumenthal-Getoor,

Comment: To be asked

Keywords: Polar sets, Semi-polar sets, Excessive functions

Nature: Original

Retrieve article from Numdam

VII: 07, 51-57, LNM 321 (1973)

Une conjecture sur les ensembles semi-polaires (Markov processes)

For a right process satisfying the absolute continuity hypothesis and assuming singletons are semi-polar sets, it is conjectured that a (nearly-)Borel set is semipolar if and only if it does not contain uncountable families of disjoint, non-polar compact sets. This statement implies that two processes which have the same polar sets also have the same semi-polar sets

Comment: The conjecture can be proved, using a general result of Mokobodzki, see 1238

Keywords: Polar sets, Semi-polar sets

Nature: Original

Retrieve article from Numdam

IX: 29, 495-495, LNM 465 (1975)

Une propriété des ensembles semi-polaires (Markov processes)

It is shown that semi-polar sets are exactly those which have potential 0 for all continuous additive functionals (or for all time-changed processes)

Keywords: Semi-polar sets

Nature: Original

Retrieve article from Numdam

X: 29, 544-544, LNM 511 (1976)

Correction à des exposés de 1973/74 (Descriptive set theory)

Corrections to 915 and 918

Keywords: Analytic sets, Semi-polar sets, Suslin spaces

Nature: Original

Retrieve article from Numdam

XII: 38, 509-511, LNM 649 (1978)

Appendice à l'exposé de Mokobodzki (Measure theory, General theory of processes)

Some comments on 1237: a historical remark, a relation with a result of Talagrand, the inclusion of a converse (due to Horowitz) to the case of finite sections, and the solution to the conjecture from 707

Keywords: Sets with countable sections, Semi-polar sets

Nature: Original

Retrieve article from Numdam

XII: 43, 564-566, LNM 649 (1978)

Deux propriétés des ensembles minces (abstraits) (Descriptive set theory)

Given a class ${\cal S}$ of Borel sets understood as ``small'' sets, the class ${\cal L}$ consisting of their conplements understood as ``large'' sets, a set $A$ is said to be ${\cal S}$-thin if does not contain uncountably many disjoint ``large'' sets. For instance, if ${\cal S}$ is the class of polar sets, then thin sets are the same as semi-polar sets. Two general theorems are proved here on thin sets

Keywords: Thin sets, Semi-polar sets, Essential suprema

Nature: Original

Retrieve article from Numdam