Decomposition of Measures

Carlos S. Kubrusly
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 7 in Essentials of Measure Theory, 2015, pp 109-129 from Springer

Abstract: Abstract Take a signed measure $$\nu: \mathcal{X}\!\rightarrow \mathbb{R}$$ on a $$\sigma$$ -algebra $$\mathcal{X}$$ of subsets of a set X. According to Definition 2.3, signed measures are real-valued set functions. We saw in Section 2.2 that if $$\mu$$ and $$\lambda$$ are finite measures, then $$\nu =\mu -\lambda$$ is a signed measure. In this section we show that all signed measures $$\nu$$ admit a decomposition into a difference of two finite measures.

Keywords: Measurable Space; Signed Measure; Measurable Subset; Finite Measure; Small Positive Integer (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22506-7_7

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