It is well known that the Lagrangian formulation of the path integral has been made rigorous, via the Wiener measure and/or the Trottier product formula. I haven't seen mathematicians discuss the hamiltonian version though, where one integrates over paths in phase space instead. Physicists seem to use it, but has it been made rigorous?
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I wonder if this question could be acceptable for MathOverflow too... – Alexey Oct 12 '18 at 19:22