| As is always the case, the subsets of a certain set can be used as the basic tools to investigate the characteristics and properties of the set.; The aim of this thesis is to investigate the certain types of lattice measures with emphasis on regular measures which play the important role to characterize the lattice measure spaces.; In Chapter 1, we just present most of the definitions, terminology and notations used throughout this work.; In Chapter 2, we mainly deal with the regular lattice measures and related problems such as regularity, equivalence, normality and compactness conditions. In addition, we touch on the fundamentals of the Wallman topology. Then in the last section, separation of lattices are treated. Essentially, parts of this chapter are known results and will serve as the background for those that follow.; In the final Chapter, we focus our attention on the relations between types of lattice measures with emphasis on regular outer measures and also on the relations between the spaces on which those measures are defined. Moreover, we deal first with non-trivial zero-one valued measures and then more general measures. In particular, we consider those which satisfy certain smoothness conditions.; In order to carry out this analysis we consider certain outer measures {dollar}muspprime{dollar} and {dollar}musp{lcub}primeprime{rcub}{dollar} associated with a measure {dollar}mu{dollar} and try to characterize lattice properties and smoothness properties of measures in terms of these. |
