Hahn Decomposition Theorem of Signed Lattice Measure - Mathematics > Classical Analysis and ODEs

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Abstract: 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, wewill show that the Hahn Decomposition Theorem decomposes any space X into apositive lattice A and a negative Lattice B such that $A \vee B$ =X and thesigned Lattice measure of $A \wedge B$ is 0.

Autor: Jun Tanaka

Fuente: https://arxiv.org/