Abstract
A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence theta = {k(r)}, a sequence {x(k)} is lacunary statistical bounded if and only if for 'almost all k w.r.t theta', the values x(k) coincide with those of a bounded sequence. Apart from studying various algebraic properties and computing the Kothe-Toeplitz duals of the space S-theta(b) of all lacunary statistical bounded sequences, a decomposition theorem is also established. We characterize those theta for which S-theta(b) = S(b). Finally, we give a general description of inclusion between two arbitrary lacunary methods of statistical boundedness.