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In this paper we prove that the four-point function of massive$\vp_4^4$-theory is continuous as a function of its independent externalmomenta when posing the renormalization condition for the (physical) masson-shell. The proof is based on integral representations derived inductivelyfrom the perturbative flow equations of the renormalization group. It closes alongstanding loophole in rigorous renormalization theory in so far as it showsthe feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two  explanatory paragraphs adde

CONTINUITY OF THE FOUR-POINT FUNCTION OF MASSIVE $\varphi_{4}^{4}$-THEORY ABOVE THRESHOLD