Review of Probability Theory

  • Ettore Vitali
  • Mario Motta
  • Davide Emilio Galli
Part of the UNITEXT for Physics book series (UNITEXTPH)


This chapter provides a self-contained review of the foundations of probability theory, in order to fix notations and introduce mathematical objects employed in the remaining chapters. In particular we stress the notions of measurability, related to what it is actually possible to observe when performing an experiment, and statistical independence. We present several tools to deal with random variables; in particular we focus on the normal random variables, a cornerstone in the theory of random phenomena. We conclude presenting the law of large numbers and the central limit theorem.


Probability theory Probability spaces Random variables Probability laws Law of large numbers Central limit theorem 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ettore Vitali
    • 1
  • Mario Motta
    • 2
  • Davide Emilio Galli
    • 3
  1. 1.Department of PhysicsCollege of William and MaryWilliamsburgUSA
  2. 2.Division of Chemistry and Chemical EngineeringCalifornia Institute of TechnologyPasadenaUSA
  3. 3.Department of PhysicsUniversity of MilanMilanItaly

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