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Lebesgue Decomposition and its Uniqueness of a Signed Lattice Measure

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Author(s): D.V.S.R. Anil Kumar | J. Venkateswara Rao | Putcha V.S. Anand | T. Nageswara Rao

Journal: Asian Journal of Algebra
ISSN 1994-540X

Volume: 5;
Issue: 2;
Start page: 34;
Date: 2012;
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Keywords: positive and negative parts of v | measure | o- finite measure | Lattice | measurable function and finite measure | lattice measure space

ABSTRACT
This study explored the concept of Lebesgue decomposition and its uniqueness of a signed lattice measure. It originates the concepts of lattice measure space, lattice finite measure, lattice finite measure space and σ-finite measure. Further instigation was done on σ-finite measure space, positive and negative parts of v, mutually singular lattice measures and absolutely continuous lattice measures. In addition the well known Lebesgue decomposition and its uniqueness for signed lattice measure were obtained.
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