Advertisement

Probability and Random Variables

  • Bing LiEmail author
  • G. Jogesh Babu
Chapter
  • 2k Downloads
Part of the Springer Texts in Statistics book series (STS)

Abstract

A brief outline of the important ideas and results from classical theory of measure and probability are presented in this chapter. This is not intended for the first reading of the subjects, but rather as a review and a reference. In the last section we lay out some basic notations that will be repeatedly used throughout the book.

References

  1. Billingsley, P. (1995). Probablity and Measure. Third Edition. Wiley.Google Scholar
  2. Conway, J. B. (1990). A course in functional analysis. Second edition. Springer, New York.Google Scholar
  3. Halmos, P. R. and Savage, L. J. (1949). Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics. The Annals of Mathematical Statistics, 20, 225–241.MathSciNetCrossRefGoogle Scholar
  4. Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung (in German). Berlin: Julius Springer. Translation: Foundations of the Theory of Probability (2nd ed.). New York: Chelsea. (1956).Google Scholar
  5. Perlman, M. D. (1974). Jensen’s inequality for a convex vector-valued function on an infinite-dimensional space. Journal of Multivariate Analysis, 4, 52–65.MathSciNetCrossRefGoogle Scholar
  6. Rudin, W. (1987). Real and Complex Analysis. Third Edition. McGraw-Hill, Inc.Google Scholar
  7. Vestrup, E. M. (2003). The Theory of Measures and Integration. Wiley.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsPenn State UniversityUniversity ParkUSA

Personalised recommendations