Scale-invariant measurability in abstract Wiener spaces

Dong M. Chung

Vol. 130 (1987), No. 1, 27–40

DOI: 10.2140/pjm.1987.130.27

Abstract

In this paper, we first prove a limit theorem for a sequence of quadratic functionals 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 scale-invariant measurability and translations in an abstract Wiener space.

Mathematical Subject Classification 2000

Primary: 28C20

Secondary: 46G12, 60B11, 60F17

Milestones

Received: 25 April 1986

Revised: 2 December 1986

Published: 1 November 1987