Vol. 83, No. 1, 1979

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Scale-invariant measurability in Wiener space

Gerald William Johnson and David Lee Skoug

Vol. 83 (1979), No. 1, 157–176

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
Received: 19 October 1978
Revised: 20 December 1978
Published: 1 July 1979
Gerald William Johnson
David Lee Skoug