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

A mistake in a paper by Osterwalder et al. (see abstr. A43062 of 1973) is corrected in the following sense: thanks to these axioms the Euclidean Schwinger functions S/sub n/ can be analytically continued to the corresponding Wightman functions W/sub 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. (7 refs).