Stochastic L2-Integration with a Locally Compact Time-Region

This paper contains some results about the theory of stochastic L²-Integration with a general time-region. The starting point of our theory is not a family of σ-algebras but, more generally, a family of projection operators in the Hilbert space of all square integrable random functions. To do this we use some Hilbert space analysis as well as the methods of Metivier and Pellaumail.