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Essentials of Probability Theory and Mathematical Statistics

  • Robert S. Liptser
  • Albert N. Shiryaev
Chapter
Part of the Applications of Mathematics book series (SMAP, volume 5)

Abstract

According to Kolmogorov’s axiomatics the primary object of probability theory is the probability space (Ω,F, P). Here (Ω, F) denotes measurable space, i.e., a set Ω consisting of elementary events ω, with a distinguished system F of its subsets (events), forming a σ-algebra, and P denotes a probability measure (probability) defined on sets in F.

Keywords

Brownian Motion Random Process Brownian Motion Process Integrable Random Variable Markov Time 
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-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Robert S. Liptser
    • 1
  • Albert N. Shiryaev
    • 2
  1. 1.Department of Electrical Engineering SystemsTel Aviv UniversityTel AvivIsrael
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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