Convergence of Stochastic Processes pp 43-63 | Cite as

# Convergence in Distribution in Euclidean Spaces

Chapter

## Abstract

Convergence is distribution of a sequence .

*X*_{ n }of real random variable is traditionally defined to mean convergence of distribution functions at each continuity point of the limit distribution function:$$\mathbb{P}\{ X_n \leqslant x\} \to \mathbb{P}\{ X \leqslant x\} \,\text{whenever}\,\mathbb{P}\{ X = x\} = 0$$

## Keywords

Probability Measure Characteristic Function Euclidean Space Random Vector Central Limit Theorem
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## Copyright information

© Springer-Verlag New York Inc. 1984