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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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1898-9934
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Volume 17, Issue 2

Issues

Hopf Extension Theorem of Measure

Noboru Endou / Hiroyuki Okazaki / Yasunari Shidama
Published Online: 2009-07-14 | DOI: https://doi.org/10.2478/v10037-009-0018-6

Hopf Extension Theorem of Measure

The authors have presented some articles about Lebesgue type integration theory. In our previous articles [12, 13, 26], we assumed that some σ-additive measure existed and that a function was measurable on that measure. However the existence of such a measure is not trivial. In general, because the construction of a finite additive measure is comparatively easy, to induce a σ-additive measure a finite additive measure is used. This is known as an E. Hopf's extension theorem of measure [15].

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About the article


Published Online: 2009-07-14

Published in Print: 2009-01-01


Citation Information: Formalized Mathematics, Volume 17, Issue 2, Pages 157–162, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0018-6.

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