Spectral integrals of Bernoulli generalized functionals

Let S⊂L2⊂S∗ be the Gel'fand triple over Bernoulli space, where elements of S∗ are called generalized functionals. In this paper, we define integrals functionals with respect to a spectral measure (projection operator-valued measure) in framework S⊂L2⊂S∗, and examine their fundamental properties. New notions introduced, several results obtained examples also shown.