This paper is a study on Complex integrable lattice functions and wfree lattices. It initiates the concepts of complex integrable lattice function, positive and negative separations of &mgr; and establishes the separation properties of complex integrable lattice functions. Also it introduce the concepts of free lattice, &mgr;-free lattice and demonstrate that &mgr; is a measure on &bgr;, &mgr; is a free lattice in &bgr;, &bgr; is a &mgr;-free lattice of &agr; (L). Also it was defined the concept almost free lattice and finally confirm that every almost free lattice is a complex integrable lattice function and a &agr;-additive. [ABSTRACT FROM AUTHOR]