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Take a signed measure ν : X → ℝ on a σ-algebra X of subsets of a set X (cf. Definition 2.3). We saw in Section 2.2 that if μ and η are finite measures, then ν = μ − η is a signed measure. In this section we show that all signed measures ν admit a decomposition into a difference of two finite measures.

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Decomposition of Measures

  • 章节

  • 发表日期：

    2026年

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  • Carlos S. Kubrusly

摘要

Take a signed measure ν : X → ℝ on a σ-algebra X of subsets of a set X (cf. Definition 2.3). We saw in Section 2.2 that if μ and η are finite measures, then ν = μ − η is a signed measure. In this section we show that all signed measures ν admit a decomposition into a difference of two finite measures.