Slutsky's theorem

In probability theory, Slutsky's theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables.

[1] The theorem was named after Eugen Slutsky.

[2] Slutsky's theorem is also attributed to Harald Cramér.

converges in distribution to a random element

Notes: This theorem follows from the fact that if Xn converges in distribution to X and Yn converges in probability to a constant c, then the joint vector (Xn, Yn) converges in distribution to (X, c) (see here).