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2009 | 17 | 2 | 157-162
Tytuł artykułu

Hopf Extension Theorem of Measure

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].
Słowa kluczowe
Wydawca
Rocznik
Tom
17
Numer
2
Strony
157-162
Opis fizyczny
Daty
wydano
2009-01-01
online
2009-07-14
Twórcy
autor
  • Gifu National College of Technology, Japan
  • Shinshu University, Nagano, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [3] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.
  • [4] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.
  • [5] Józef Białas. Several properties of the σ-additive measure. Formalized Mathematics, 2(4):493-497, 1991.
  • [6] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
  • [7] Józef Białas. Properties of Caratheodor's measure. Formalized Mathematics, 3(1):67-70, 1992.
  • [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [12] Noboru Endou, Keiko Narita, and Yasunari Shidama. The Lebesgue monotone convergence theorem. Formalized Mathematics, 16(2):167-175, 2008, doi:10.2478/v10037-008-0023-1.[Crossref]
  • [13] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006, doi:10.2478/v10037-006-0008-x.[Crossref]
  • [14] Adam Grabowski. On the Kuratowski limit operators. Formalized Mathematics, 11(4):399-409, 2003.
  • [15] P. R. Halmos. Measure Theory. Springer-Verlag, 1987.
  • [16] Krzysztof Hryniewiecki. Recursive definitions. Formalized Mathematics, 1(2):321-328, 1990.
  • [17] Franz Merkl. Dynkin's lemma in measure theory. Formalized Mathematics, 9(3):591-595, 2001.
  • [18] Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.
  • [19] Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
  • [20] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  • [21] Karol Pąk. The Nagata-Smirnov theorem. Part II. Formalized Mathematics, 12(3):385-389, 2004.
  • [22] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [24] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [25] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [26] Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, and Hiroyuki Okazaki. Inferior limit, superior limit and convergence of sequences of extended real numbers. Formalized Mathematics, 15(4):231-236, 2007, doi:10.2478/v10037-007-0026-3.[Crossref]
  • [27] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Set sequences and monotone class. Formalized Mathematics, 13(4):435-441, 2005.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-009-0018-6
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