Hahn Decomposition Theorem of Signed Lattice Measure

Details Hahn Decomposition Theorem of Signed Lattice Measure Hahn Decomposition Theorem of Signed Lattice Measure

2009-05-31

arxiv.org/abs/0906.0147v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this paper, we will define a signed Lattice measure on $\sigma$-algebras,
as well as give the definition of positive and negative Lattice. Herein, we
will show that the Hahn Decomposition Theorem decomposes any space X into a
positive lattice A and a negative Lattice B such that $A \vee B$ =X and the
signed Lattice measure of $A \wedge B $ is 0.

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