In reference to this question Lebesgue Decomposition Theorem and in general I would like to ask why does one care about the decomposition of a measure? What it helps in any way with respect to probability theory or whatever. Is there a straight forward technique by which one decomposes a measure in three-part as mentioned in the answer of the above question? A nice reference reading would be grand or otherwise. Thanks so much!
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The Lebesgue Decomposition theorem is used to decompose the spectrum of a linear operator,and it is used in the Levy-Ito Decomposition. – Angela Pretorius Nov 18 '19 at 13:01
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ah! long wiki read! waiting for some Philosophical answer Thanks anyway! I will read them! – Myshkin Nov 18 '19 at 13:18