``Lebesgue measure'' on , II

Author:
Richard L. Baker

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2577-2591

MSC (2000):
Primary 28A35, 28C10, 81D05

Published electronically:
April 21, 2004

MathSciNet review:
2054783

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the set of real numbers, and define . We construct a complete measure space where the -algebra contains the Borel subsets of , and is a translation-invariant measure such that for any measurable rectangle , if , then , where is Lebesgue measure on . The measure is not -finite. We prove three Fubini theorems, namely, the Fubini theorem, the mean Fubini-Jensen theorem, and the pointwise Fubini-Jensen theorem. Finally, as an application of the measure , we construct, via selfadjoint operators on , a ``Schrödinger model'' of the canonical commutation relations: , , .

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Additional Information

**Richard L. Baker**

Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242

Email:
baker@math.uiowa.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07372-1

Keywords:
Canonical commutation relations,
Elliott-Morse measures,
Fubini theorem,
Fubini-Jensen theorem,
infinite-dimensional Lebesgue measure,
invariant measures,
Schr\"{o}dinger model

Received by editor(s):
August 16, 1994

Received by editor(s) in revised form:
March 21, 2003

Published electronically:
April 21, 2004

Communicated by:
David R. Larson

Article copyright:
© Copyright 2004
American Mathematical Society