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Lebesgue decomposition via Riesz orthogonal decomposition. (English) Zbl 1374.28001

Summary: The aim of this short note is to give a simple proof of the classical Lebesgue decomposition theorem of measures via the Riesz orthogonal decomposition theorem of Hilbert spaces.

MSC:

28A12 Contents, measures, outer measures, capacities
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
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