This paper describes a class of null sets; point, lattice measure of a point and lattice semi-finite measure were introduced. Here it has been derived a result that in a countable Boolean lattice the lattice measure of any two points are either disjoint or identical also the class of all points in countable Boolean lattice is countable and proved that Any union countable of null partial lattices is null partial lattice, also established that the class of points in countable Boolean lattice is countable. It has been obtained a theorem that if a countable Boolean lattice is pointless if and only if every non empty set in countable Boolean lattice contains countable number of disjoint non-empty sets. Finally it has been observed that some elementary nature of points in a countable Boolean lattice.