Uniform Boundedness Principle

Hideki Sakurai; Hisayoshi Kunimune; Yasunari Shidama

Formalized Mathematics (2008)

  • Volume: 16, Issue: 1, page 19-21
  • ISSN: 1426-2630

Abstract

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In this article at first, we proved the lemma of the inferior limit and the superior limit. Next, we proved the Baire category theorem (Banach space version) [20], [9], [3], quoted it and proved the uniform boundedness principle. Moreover, the proof of the Banach-Steinhaus theorem is added.MML identifier: LOPBAN 5, version: 7.8.05 4.89.993

How to cite

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Hideki Sakurai, Hisayoshi Kunimune, and Yasunari Shidama. "Uniform Boundedness Principle." Formalized Mathematics 16.1 (2008): 19-21. <http://eudml.org/doc/266597>.

@article{HidekiSakurai2008,
abstract = {In this article at first, we proved the lemma of the inferior limit and the superior limit. Next, we proved the Baire category theorem (Banach space version) [20], [9], [3], quoted it and proved the uniform boundedness principle. Moreover, the proof of the Banach-Steinhaus theorem is added.MML identifier: LOPBAN 5, version: 7.8.05 4.89.993},
author = {Hideki Sakurai, Hisayoshi Kunimune, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {19-21},
title = {Uniform Boundedness Principle},
url = {http://eudml.org/doc/266597},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Hideki Sakurai
AU - Hisayoshi Kunimune
AU - Yasunari Shidama
TI - Uniform Boundedness Principle
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 1
SP - 19
EP - 21
AB - In this article at first, we proved the lemma of the inferior limit and the superior limit. Next, we proved the Baire category theorem (Banach space version) [20], [9], [3], quoted it and proved the uniform boundedness principle. Moreover, the proof of the Banach-Steinhaus theorem is added.MML identifier: LOPBAN 5, version: 7.8.05 4.89.993
LA - eng
UR - http://eudml.org/doc/266597
ER -

References

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