Lebesgue Decomposition and its Uniqueness of a Signed Lattice Measure

This study explored the concept of Lebesgue decomposition and its uniqueness of a signed lattice measure. It originates the concepts of lattice measure space, lattice finite measure, lattice finite measure space and σ-finite measure. Further instigation was done on σ-finite measure space, positive and negative parts of v, mutually singular lattice measures and absolutely continuous lattice measures. In addition the well known Lebesgue decomposition and its uniqueness for signed lattice measure were obtained.