Decompositions of spaces of measures

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1 Citation (Scopus)


Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.
Original languageEnglish
Pages (from-to)119-126
Number of pages8
JournalInfinite Dimensional Analysis Quantum Probability and Related Topics
Issue number1
Publication statusPublished - Mar 2008

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistics and Probability
  • Statistical and Nonlinear Physics

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