Infinite dimensional quasi continuity, path continuity and ray continuity of functions with fractional regularity

We prove for functions in Sobolev spaces in L-p of fractional order r over infinite dimensional spaces (p, r)-quasi continuity yields path (r/2 - 1/p) -Holder continuity if pr > 2 and ray (r - 1/p)-Holder continuity if pr > 1. We also present applications to the quasi everywhere existence of local ti mes of smooth martingales and ergodicity of the (generalized) Cameron-Marti n space. (C) 2001 Editions scientifiques et medicales Elsevier SAS. AMS cla ssification: Primary: 60H07, 31C25; Secondary: 28C20, 46G12.