Measure Theory pp 145-156 | Cite as

Signed Measures

  • J. L. Doob
Part of the Graduate Texts in Mathematics book series (GTM, volume 143)

Abstract

Signed measures, defined in Section III.l, have values either in (-∞,+∞] or [-∞,+∞), to avoid the possibility of adding +∞ to -∞. It will be shown in Section 2 that a signed measure is actually bounded on the side where it is finite. For a signed measure space (S, S,λ,), the signed measure λ has its values in (-∞,+∞] if and only if λ(S) > -∞, its values in [-∞,+∞) if and only if λ(S) < +∞, and λ is finite valued if and only if λ(S) is finite.

Keywords

Radon 

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • J. L. Doob
    • 1
  1. 1.UrbanaUSA

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