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Vol. 1, Issue 10, Part F (2015)
Lebesgue Decomposition Theorem and its extension to Signed measures
Lebesgue Decomposition Theorem and its extension to Signed measures
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Abstract
By Lebesgue Decomposition Theorem for any ߪ െfinite measurable space (X, ࣛ,ߤሻ we prove that if ݒ be any other ߪ െfinite measure on ࣛ then there exist a unique pair of measures (ݒ, ଴ݒଵ) such that ݒ = ݒ ൅ ଴ݒଵ and ݒ ଴٣ ߤ and ݒଵ ≪ ߤ .The result can be extended to signed measures also.
By Lebesgue Decomposition Theorem for any ߪ െfinite measurable space (X, ࣛ,ߤሻ we prove that if ݒ be any other ߪ െfinite measure on ࣛ then there exist a unique pair of measures (ݒ, ଴ݒଵ) such that ݒ = ݒ ൅ ଴ݒଵ and ݒ ଴٣ ߤ and ݒଵ ≪ ߤ .The result can be extended to signed measures also.
Pages: 372-374 | 862 Views 134 Downloads
How to cite this article:
Parvinder Singh. Lebesgue Decomposition Theorem and its extension to Signed measures. Int J Appl Res 2015;1(10):372-374.
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