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A remark on Slutsky’s theorem. (English) Zbl 0915.60004

Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXII. Berlin: Springer. Lect. Notes Math. 1686, 313-315 (1998).
The author proves a necessary and sufficient condition that assures that whenever \(X_n\) is a sequence of random variables that converges in probability to some random variable \(X\), then for each Borel function \(f\) we also have that \(f(X_n)\) tends to \(f(X)\) in probability.
For the entire collection see [Zbl 0893.00035].

MSC:

60A10 Probabilistic measure theory
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
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