The extension of bounded lattice continuous functions on an arbitrary set X to the
set of lattice regular zero-one measures on an algebra generated by a lattice (a Wallman-type space)
is investigated.Next the subset of lattice regular zero-one measures on an algebra generated by a lattice which
integrates all lattice continuous functions on X is introduced and various properties of it are
presented.Finally conditions are established using repleteness criteria whereby the space of lattice regular
zero-one measures on an algebra generated by a lattice which are countably additive (a Wallman-type
space) is realcompact.