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Jan 31 at 10:59 comment added gmvh P. Cartier and C. DeWitt-Morette, Functional Integration, Cambridge University Press 2006.
Jan 31 at 10:56 comment added lcv I think in general properly defining the (functional) measure is hard. What one can do is define it perturbatively around a manageable case, i.e. the Gaussian one. The book by Glimm and Jaffe may be a possible entry (though it's a bit old).
Jan 31 at 10:50 history edited gmvh CC BY-SA 4.0
Fixed typos, improved MathJax
Jan 31 at 3:08 comment added Michael Engelhardt I don't know about "It is usually said ...". What I hear usually said among physicists is that in the path integral, the set of smooth functions is of measure zero, and the integral is dominated by rough paths. Smooth paths maybe if you're doing a semiclassical approximation.
Jan 31 at 0:07 history asked 0x11111 CC BY-SA 4.0