Slutsky's theorem

The Slutsky theorem, developed by Yevgeny Slutsky (E. Slutsky ), is a mathematical theorem in the field of probability theory, which concerns the convergence of random variables.

Theorem

If the sequence of random variables tends to infinity converges to the random variable in distribution and converge the sequences of random variables and the values ​​of and in probability, then the function converges to in distribution. In short: