Advertisement

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

Measure Space Signed Measure Measurable Subset Finite Measure Jordan Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

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

Personalised recommendations