Scale-invariant measurability in abstract Wiener spaces

Abstract

In this paper, we first prove a limit theorem for a sequence of quadratic functional on an abstract Wiener space which generalizes a Cameron-Martin limit theorem in the Wiener space; and next we prove a version of a converse measurability theorem for the Wiener space in the setting of abstract Wiener spaces. Using these results, we discuss scaleinvariant measurability and translations in an abstract Wiener space.