Integration in Hilbert Space

Integration in function spaces arose in probability theory when a gen­ eral theory of random processes was constructed. Here credit is cer­ tainly due to N. Wiener, who constructed a measure in function space, integrals-with respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe­ nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establis