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VII: 19, 198-204, LNM 321 (1973)

**MEYER, Paul-André**

Limites médiales d'après Mokobodzki (Measure theory, Functional analysis)

Given a sequence of (classes of) random variables on a probability space which converges in some of the standard ways of measure theory, the problem is to find some universal method (independent from the underlying probability) to identify its limit. For convergence in probability, and thus for all strong $L^p$ topologies, Mokobodzki had discovered the procedure of rapid ultrafilters (see 304). The same problem is now solved for weak convergences, using a special kind of Banach limits

Comment: The paper contains a few annoying misprints, in particular p.199 line 9*s.c;s.* should be deleted and line 17 *atomique * should be *absolument continu.* For a misprint-free version see Dellacherie-Meyer, *Probabiliés et Potentiel,* Volume C, Chapter X, **55**--57

Keywords: Continuum axiom, Weak convergence of r.v.'s, Medial limit

Nature: Exposition

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Limites médiales d'après Mokobodzki (Measure theory, Functional analysis)

Given a sequence of (classes of) random variables on a probability space which converges in some of the standard ways of measure theory, the problem is to find some universal method (independent from the underlying probability) to identify its limit. For convergence in probability, and thus for all strong $L^p$ topologies, Mokobodzki had discovered the procedure of rapid ultrafilters (see 304). The same problem is now solved for weak convergences, using a special kind of Banach limits

Comment: The paper contains a few annoying misprints, in particular p.199 line 9

Keywords: Continuum axiom, Weak convergence of r.v.'s, Medial limit

Nature: Exposition

Retrieve article from Numdam