Quick search | Browse volumes | |

I: 07, 163-165, LNM 39 (1967)

**MEYER, Paul-André**

Sur un théorème de Deny (Potential theory, Measure theory)

In the potential theory of a resolvent which satisfies the absolute continuity hypothesis, every sequence of excessive functions contains a subsequence which converges except on a set of potential zero. It is also proved that a sequence which converges weakly in $L^1$ but not strongly must oscillate around its limit

Comment: a version of this result in classical potential theory was proved by Deny,*C.R. Acad. Sci.*, **218**, 1944. The cone of excessive functions possesses good compactness properties, discovered by Mokobodzki. See Dellacherie-Meyer, *Probabilités et Potentiel,* end of chapter XII

Keywords: A.e. convergence, Subsequences

Nature: Original

Retrieve article from Numdam

IV: 08, 76-76, LNM 124 (1970)

**DELLACHERIE, Claude**

Un lemme de théorie de la mesure (Measure theory)

A lemma used by Erdös, Kesterman and Rogers (*Coll. Math.,* **XI**, 1963) is reduced to the fact that a sequence of bounded r.v.'s contains a weakly convergent subsequence

Keywords: Convergence in norm, Subsequences

Nature: Original proofs

Retrieve article from Numdam

VI: 04, 72-89, LNM 258 (1972)

**CHATTERJI, Shrishti Dhav**

Un principe de sous-suites dans la théorie des probabilités (Measure theory)

This paper is devoted to results of the following kind: any sequence of random variables with a given weak property contains a subsequence which satisfies a stronger property. An example is due to Komlós: any sequence bounded in $L^1$ contains a subsequence which converges a.s. in the Cesaro sense. Several results of this kind, mostly due to the author, are presented without detailed proofs

Comment: See 1302 for extensions to the case of Banach space valued random variables. See also Aldous,*Zeit. für W-theorie,* **40**, 1977

Keywords: Subsequences, Central limit theorem, Law of the iterated logarithm

Nature: Exposition

Retrieve article from Numdam

XIII: 02, 4-21, LNM 721 (1979)

**CHATTERJI, Shrishti Dhav**

Le principe des sous-suites dans les espaces de Banach (Banach space valued random variables)

The ``principle of subsequences'' investigated in the author's paper 604 says roughly that any suitably bounded sequence of r.v.'s contains a subsequence which in some respect ``looks like'' a sequence of i.i.d. random variables. Extensions are considered here in the case of Banach space valued random variables. The paper has the character of a preliminary investigation, though several non-trivial results are indicated (one of them in the Hilbert space case)

Keywords: Subsequences

Nature: Original

Retrieve article from Numdam

Sur un théorème de Deny (Potential theory, Measure theory)

In the potential theory of a resolvent which satisfies the absolute continuity hypothesis, every sequence of excessive functions contains a subsequence which converges except on a set of potential zero. It is also proved that a sequence which converges weakly in $L^1$ but not strongly must oscillate around its limit

Comment: a version of this result in classical potential theory was proved by Deny,

Keywords: A.e. convergence, Subsequences

Nature: Original

Retrieve article from Numdam

IV: 08, 76-76, LNM 124 (1970)

Un lemme de théorie de la mesure (Measure theory)

A lemma used by Erdös, Kesterman and Rogers (

Keywords: Convergence in norm, Subsequences

Nature: Original proofs

Retrieve article from Numdam

VI: 04, 72-89, LNM 258 (1972)

Un principe de sous-suites dans la théorie des probabilités (Measure theory)

This paper is devoted to results of the following kind: any sequence of random variables with a given weak property contains a subsequence which satisfies a stronger property. An example is due to Komlós: any sequence bounded in $L^1$ contains a subsequence which converges a.s. in the Cesaro sense. Several results of this kind, mostly due to the author, are presented without detailed proofs

Comment: See 1302 for extensions to the case of Banach space valued random variables. See also Aldous,

Keywords: Subsequences, Central limit theorem, Law of the iterated logarithm

Nature: Exposition

Retrieve article from Numdam

XIII: 02, 4-21, LNM 721 (1979)

Le principe des sous-suites dans les espaces de Banach (Banach space valued random variables)

The ``principle of subsequences'' investigated in the author's paper 604 says roughly that any suitably bounded sequence of r.v.'s contains a subsequence which in some respect ``looks like'' a sequence of i.i.d. random variables. Extensions are considered here in the case of Banach space valued random variables. The paper has the character of a preliminary investigation, though several non-trivial results are indicated (one of them in the Hilbert space case)

Keywords: Subsequences

Nature: Original

Retrieve article from Numdam