## Quick Reference

A sequence of random variables *x*_{1},…, *x*_{n},… converges in probability to a random variable *x* if for every positive number ε the probability of the (Euclidean) distance between *x*_{n} and *x* exceeding ε converges to zero as *n* tends to infinity, sofor every ε > 0. This means that, if we consider a sequence of probabilities, *P*_{n} = *P*[|*x*_{n} − *x*| ≥ ε], then starting from some *n*_{0} each probability in this sequence is arbitrarily small. In particular, *x* can be a constant. Convergence in probability implies convergence in distribution (the converse does not hold, in general).

*Subjects:*
Economics.

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