Abstract
A notion of dimensional reduction for functional measures indexed by bounded rectangles in Euclidean spaces is introduced. For a general class of functional measures absolutely continuous with respect to a Gaussian functional measure, a sufficient condition for the dimensional reducibility is given. It is shown that functional measures associated with the P( φ) v - or the Albeverio-Høegh-Krohn models in Euclidean quantum field theories are dimensionally reducible, so that functional integrals with respect to them can be approximated by one dimensional integrals. As an application, a limit theorem for quantum partition functions of the models in the two dimensional space-time is proved.
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