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An Application of Gaussian Measures to Functional Analysis

  • Daniel W. StroockEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

In a variety of settings, it is shown that all Borel measurable, linear maps from one locally convex topological vector space to another must be continuous. When the image space is Polish, this gives a proof of L. Schwartz’s Borel graph theorem. The proof is based on a simple probabilistic argument and, except for the application to Schwartz’s theorem, avoids the descriptive set theory used in previous treatments of such results.

Received 6/14/2011; Accepted 11/22/2011; Final 11/22/2011

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.M.I.T, 2-272CambridgeUSA

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