Abstract
A signed measure on a measurable space is a set function which has all the properties of a measure, except that of non-negativity. It is shown that signed measures are essentially got by taking the difference of two measures. The notion of absolute continuity is introduces and the famous Radon-Nikodym theorem is proved for σ-finite signed measures. The notion of singularity, of one measure with respect to another, is studied.
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© 2019 Hindustan Book Agency 2019 and Springer Nature Singapore Pte Ltd.
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Kesavan, S. (2019). Signed measures. In: Measure and Integration. Texts and Readings in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-6678-9_9
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DOI: https://doi.org/10.1007/978-981-13-6678-9_9
Publisher Name: Springer, Singapore
Online ISBN: 978-981-13-6678-9
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