Borel Sets and Measures

  • Alexander S. Kechris
Part of the Graduate Texts in Mathematics book series (GTM, volume 156)


Let (X,S) be a measurable space. A measure on (X,S) is a map µ: S → [0,∞] such that µ (Ø) = 0 and \(\mu \left( {\bigcup\nolimits_n {{A_n}} } \right) = {\Sigma _n}\mu \left( {{A_n}} \right)\)for any pairwise disjoint family {An} \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \subset } \)S. A measure space is a triple (X,S,µ), where (X,S) is a measurable space and µ is a measure on (X,S). We often write (X,µ) when there is no danger of confusion.


Boolean Algebra Borel Measure Polish Space Inverse Limit Probability Borel Measure 
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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Alexander S. Kechris
    • 1
  1. 1.Alfred P. Sloan Laboratory of Mathematics and Physics Mathematics 253-37California Institute of TechnologyPasadenaUSA

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