Laws of Large Numbers

  • Valentin V. Petrov
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 82)


We shall consider a sequence of random variables {X n ; n = 1, 2, ...}. By definition, this sequence converges in probability to the random variable X if P(│X n X│ ≧ ε) → 0 for every fixed ε > 0. In this case we use the notation \({X_n}\;\xrightarrow{P}\;X\).


Independent Random Variable Common Distribution Finite Variance Arbitrary Positive Constant Common Distribution Function 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1975

Authors and Affiliations

  • Valentin V. Petrov
    • 1
  1. 1.Leningard UniversityLeningradUSSR

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