The study of measures and integrals on infinite-dimensional spaces arose from the theory of stochastic processes, particularly the theory of Wiener processes. In recent years, the subject has been intimately connected with research on characteristic functionals, limit theorems, sample spaces, and generalized stochastic processes. Even more noteworthy is the fact that questions of integration on infinite-dimensional spaces have, during the last ten-odd years, appeared in many scientific fields, such as quantum mechanics, quantum field theory, statisticaI physics, thermodynamics of irreversible processes, turbulence theory, atomic reactor computations, and coding problems. However, the application of integration on infinite-dimensional spaces to these fields has encountered many profound difficulties, and a lack of adequate techniques. Thus, it seems that further study of this new subject is amply justified.
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