Modes of Convergence

  • Jiming JiangEmail author
Part of the Springer Texts in Statistics book series (STS, volume 0)


In this chapter we discuss different types of convergence in probability and statistics. Types of convergence have already been introduced. They are convergence in probability and convergence in distribution. In addition, we introduce other types of convergence, such as almost sure convergence and L p convergence. We discuss properties of different types of convergence, the connections between them, and how to establish these properties. The discussion will mainly focus on the case of univariate random variables. However, most of the results presented here can be easily extended to the multivariate situation.


Dominate Convergence Theorem Asymptotic Variance Cell Frequency Cell Probability Cantelli Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of CaliforniaDavisUSA

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