University · Mathematics · Measure Theory and Lebesgue Integration

The Radon-Nikodym Theorem and Signed Measures

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Signed measures, the Hahn and Jordan decompositions, absolute continuity between measures, and the Radon-Nikodym theorem, which guarantees a density function relating one measure to another -- with its historical origin in the work of Johann Radon (1913) and Otto Nikodym (1930).

Inhaltsübersicht

  • Signed Measures and the Hahn Decomposition
  • The Jordan Decomposition and Total Variation
  • Absolute Continuity and the Radon-Nikodym Theorem
  • Applications, History, and the Lebesgue Decomposition
Diagram of positive and negative sets partitioning a space under a signed measure
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Learn The Radon-Nikodym Theorem and Signed Measures — Measure Theory and Lebesgue Integration Mathematics | Summary, Flashcards & Quiz