Essentials of probability theory and mathematical statistics

  • R. S. Liptser
  • A. N. Shiryayev
Part of the Applications of Mathematics book series (SMAP, volume 5)


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


Random Process Mathematical Statistic Nonnegative Random Variable Uniform Integrability Brownian Motion Process 
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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • R. S. Liptser
    • 1
  • A. N. Shiryayev
    • 2
  1. 1.Institute for Problems of Control TheoryMoscowUSSR
  2. 2.Institute of Control SciencesMoscowUSSR

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