Characterization of Lattice Measurable Functions on Product Lattices

This study introduce and advance the characteristics of S-lattice measurable function and T-lattice measurable function. It has been proved that the integrations of these lattice measurable functions are made equal. Also it establishes the result that the two iterated integrals of lattice measurable functions are finite and equal. Finally, it confirms that for the lattice σ-finiteness, the Lebesgue lattice measure cannot be omitted and the condition that f is a lattice measurable with respect to the lattice σ-algebra.