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Ergodic Theory

  • Luís BarreiraEmail author
  • Claudia Valls
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

For a measure space \((X,\mathcal {A},\mu )\), show that:
  1. 1.

    if \(A, B \in \mathcal {A}\) and \(A\subseteq B\), then \(\mu (A) \le \mu (B)\);

     
  2. 2.
    if \(B_n \in \mathcal {A}\) for all \(n \in \mathbb {N}\), then
    $$ \mu \left( \bigcup _{n=1}^\infty B_n \right) \le \sum _{n=1}^\infty \mu (B_n). $$
     

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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