English

Hahn Decomposition Theorem of Signed Lattice Measure

Classical Analysis and ODEs 2009-06-02 v1

Abstract

In this paper, we will define a signed Lattice measure on σ\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 ABA \vee B =X and the signed Lattice measure of ABA \wedge B is 0.

Cite

@article{arxiv.0906.0147,
  title  = {Hahn Decomposition Theorem of Signed Lattice Measure},
  author = {Jun Tanaka},
  journal= {arXiv preprint arXiv:0906.0147},
  year   = {2009}
}
R2 v1 2026-06-21T13:08:04.118Z