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,
SubsequencesNature: 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,
SubsequencesNature: 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 logarithmNature: 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: SubsequencesNature: Original Retrieve article from Numdam
