# [Banach] Abstract of a paper by Peter A. Loeb and Erik Talvila

Dale Alspach alspach at www.math.okstate.edu
Mon Jun 21 13:05:57 CDT 2004

This is an announcement for the paper "Lusin's Theorem and Bochner
integration" by Peter A. Loeb and Erik Talvila.

Abstract: It is shown that the approximating functions used to define
the Bochner integral can be formed using geometrically nice sets, such as
balls, from a differentiation basis. Moreover, every appropriate sum of
this form will be within a preassigned $\varepsilon$ of the integral, with
the sum for the local errors also less than $\varepsilon$. All of this
follows from the ubiquity of Lebesgue points, which is a consequence of
Lusin's theorem, for which a simple proof is included in the discussion.

Archive classification: Classical Analysis and ODEs; Functional Analysis

Mathematics Subject Classification: 28A20, 28B05; 26A39

Remarks: To appear in Scientiae Mathematicae Japonicae

The source file(s), bochnerbox.tex: 34366 bytes, is(are) stored in gzipped
form as 0406370.gz with size 11kb. The corresponding postcript file has
gzipped size 52kb.

Submitted from: etalvila at math.ualberta.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/math.CA/0406370

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http://arXiv.org/abs/math.CA/0406370

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uget 0406370

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