Vol. 99, No. 1, 1982

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ISSN: 0030-8730
Realizing automorphisms of quotients of product σ-fields

Siegfried Graf

Vol. 99 (1982), No. 1, 19–30
Abstract

Let (Xα)αI be a family of Polish spaces, X = ΠαIXα, and B the product of the Borel fields of the spaces Xα. For K I let XK = ΠαKXα and let πK : X XK be the canonical projection. Moreover, let n be a σ-ideal in B satisfying the following Fubini type condition:

N n if and only if πJ1({z XJ|πIJ1({y XIJ|(z,y) N})n}) n for every nonempty J I. Then, given an automorphism Φ from Bn onto itself, there exists a bijection f : X X such that f and f1 are measurable and

[f−1(B )] = Φ([B ]), [f(B )] = Φ−1([B ])

for all B B.

Mathematical Subject Classification 2000
Primary: 28A35
Secondary: 54H13
Milestones
Received: 28 March 1980
Published: 1 March 1982
Authors
Siegfried Graf