A lattice space is defined to be an ordered pair whose first component
is an arbitrary set X and whose second component is an arbitrary lattice L of subsets
of X. A lattice space is a generalization of a topological space. The concept
of lattice normality plays an important role in the study of lattice spaces.The present work establishes various relationships between normality of
lattices of subsets of X and certain outer measures induced by measures associated
with the algebras of subsets of X generated by these lattices.