Basic Measure Theory

  • Achim Klenke
Part of the Universitext book series (UTX)


In this chapter, we lay the measure theoretic foundations of probability theory. We introduce the classes of sets (semirings, rings, algebras, σ-algebras) that allow for a systematic treatment of events and random observations. Using the measure extension theorem, we construct measures, in particular probability measures on σ-algebras. Finally, we define random variables as measurable maps and study the σ-algebras generated by certain maps.


  1. 37.
    Dudley RM (2002) Real analysis and probability. Cambridge studies in advanced mathematics, vol 74. Cambridge University Press, Cambridge. Revised reprint of the 1989 original Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Achim Klenke
    • 1
  1. 1.Institut für MathematikJohannes Gutenberg-Universität MainzMainzGermany

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