Hopf Extension Theorem of Measure

Noboru Endou; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 157-162
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama. "Hopf Extension Theorem of Measure." Formalized Mathematics 17.2 (2009): 157-162. <http://eudml.org/doc/266742>.

@article{NoboruEndou2009,
abstract = {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].},
author = {Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {157-162},
title = {Hopf Extension Theorem of Measure},
url = {http://eudml.org/doc/266742},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Noboru Endou
AU - Hiroyuki Okazaki
AU - Yasunari Shidama
TI - Hopf Extension Theorem of Measure
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 157
EP - 162
AB - 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].
LA - eng
UR - http://eudml.org/doc/266742
ER -

References

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