## 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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