Hahn Decomposition Theorem of Signed Lattice Measure
Jun Tanaka · arXiv (Cornell University) · 2009
In this paper, we will define a signed Lattice measure on $σ$-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.