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2013/2014 A Functional Analytic Proof of the Lebesgue-Darst Decomposition Theorem
Zsigmond Tarcsay
Real Anal. Exchange 39(1): 219-226 (2013/2014).


The aim of this paper is to give a functional analytic proof of the Lebesgue--Darst decomposition theorem \cite{Darst}. We show that the decomposition of a nonnegative valued additive set function into absolutely continuous and singular parts with respect to another derives from the Riesz orthogonal decomposition theorem employed in a corresponding Hilbert space.


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Zsigmond Tarcsay. "A Functional Analytic Proof of the Lebesgue-Darst Decomposition Theorem." Real Anal. Exchange 39 (1) 219 - 226, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2014

zbMATH: 1303.28005
MathSciNet: MR3261907

Primary: 28A12 , 47C05
Secondary: 46N99

Keywords: Absolute continuity , Hilbert space methods‎ , Lebesgue-Darst decomposition , Orthogonal decomposition , orthogonal projection , singularity

Rights: Copyright © 2013 Michigan State University Press

Vol.39 • No. 1 • 2013/2014
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