m at h . PR ] 9 O ct 2 00 4 CAPACITIES IN WIENER SPACE , QUASI - SURE LOWER FUNCTIONS , AND KOLMOGOROV ’ S ε - ENTROPY

We propose a set-indexed family of capacities {cap G } G⊆R + on the classical Wiener space C(R +). This family interpolates between the Wiener measure (cap {0}) on C(R +) and the standard capacity (cap R +) on Wiener space. We then apply our capacities to characterize all quasi-sure lower functions in C(R +). In order to do this we derive the following capacity estimate (Theorem 2.3) which may be of independent interest: There exists a constant a > 1 such that for all r > 0,