Abstract:
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.
