Scale-invariant measurability in Wiener space

Gerald William Johnson and David Lee Skoug

Vol. 83 (1979), No. 1, 157–176

DOI: 10.2140/pjm.1979.83.157

Abstract

The fact that change of scale is a pathological transformation in Wiener space has long been known. For many problems, this pathology causes no special difficulties. However it is sometimes necessary to consider functions of the form F(λx) where λ varies over the positive reals and x varies over Wiener space. In this setting a variety of conceptual subtleties arise. In this paper we give a framework and several results which prove useful in dealing with these difficulties. In the last section of this paper we discuss several papers in the recent literature in the light of this framework.

Mathematical Subject Classification 2000

Primary: 28C20

Secondary: 58D20, 60B11

Milestones

Received: 19 October 1978

Revised: 20 December 1978

Published: 1 July 1979