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Is it known whether Wightman's axiomatic QFT is logically equivalent to Osterwalder–Schrader...

It depends on what you mean by the Osterwalder-Schrader axioms. If you begin with a Wightman field, the Bargmann-Wightman-Hall lemma tells you that the Wightman functions are (distributional) boundary …
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Must all correlation functions come from a measure?

Just to clarify formalism, a correlation functions of a Wightman field theory cannot arise from a measure. Measures describe classical probability theories, whereas a Wightman field is noncommutative. …
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