International Journal of Applied Research
Vol. 1, Issue 10, Part F (2015)
Lebesgue Decomposition Theorem and its extension to Signed measures
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.
How to cite this article:
Parvinder Singh. Lebesgue Decomposition Theorem and its extension to Signed measures. International Journal of Applied Research. 2015; 1(10): 372-374.