On the equivalence of the Euclidean and Wightman formulation of field theory

A mistake in the paper [1] on the “Axioms for Euclidean Green's Functions” is corrected in the following sense: thanks to these axioms the Euclidean Schwinger functionsS _n can be analytically continued to the corresponding Wightman functionsW _n possessing all the correct analyticity properties and satisfying a generalized positivity condition in the complex domain. It is however suggested by the proof that their tempered behaviour near the Minkowski points cannot be guaranteed without additional assumptions.