Functional Integration on Constrained Function Spaces I: Foundations

Analogy with Bayesian inference is used to formulate constraints within a scheme for functional integration proposed by Cartier and DeWitt-Morette. According to the analogy, functional counterparts of conditional and conjugate probability distributions are introduced for integrators. The analysis leads to some new functional integration tools and methods that can be applied to the study of constrained dynamical systems. Mathematics Subject Classification: 81Q35, 46N50, 35Q40.