On characterization and properties of replete Wallman spaces

The subset of lattice regular zero-one valued measures on an algebra generated by a lattice (a Wallman-type space) which integrates all lattice continuous functions on an arbitrary setX is introduced and some properties of it are presented.Then repleteness of certain Wallman spaces is considered and used in finally establishing conditions whereby the space of lattice regular zero-one valued measures on the algebra generated by a lattice which are countably additive (a Wallman-type space) is realcompact.