Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures
[^(m)]\hat \mu
and
[(m)\tilde]\tilde \mu
on suitable lattices of the Wallman space IR(L) and another measure µ
[^(m)]\hat \mu
,
[(m)\tilde]\tilde \mu
and µ
; and try to set some new criterion for repleteness and measure repleteness.
Key words and phrases Replete and measure replete lattices - Lattice regular measure - Wallman space and remainder,
-smooth -
-smooth and tight measures - purely finitely additive measures - purely-additive measures - purely-additive measures