Abstract
Let be the Gel'fand triple over the Bernoulli space, where elements of
are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli generalized functionals with respect to a spectral measure (projection operator-valued measure) in the framework of
, and examine their fundamental properties. New notions are introduced, several results are obtained and examples are also shown.
Acknowledgements
The authors are extremely grateful to the referees for their valuable comments and suggestions on improvement of the first version of the present paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).