Jordan Decomposition and its Uniqueness of Signed Lattice Measure
Anil Kumar V, Jonnalagadda Venkateswara Rao · 2011
In this paper, we define a signed lattice measure on σ-Algebras, as well as give the definition of positive and negative lattice, positive and negative parts of ν and mutually singular lattice measures. Herein, we show that the Hann Decomposition theorem decomposes any space X into a positive lattice A and a negative lattice B such that A ∨ B = X and A ∧ B = φ. Also we prove the Jordan Decomposition theorem and its uniqueness of signed lattice measure.