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2008 | 16 | 2 | 167-175
Tytuł artykułu

The Lebesgue Monotone Convergence Theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we prove the Monotone Convergence Theorem [16].MML identifier: MESFUNC9, version: 7.8.10 4.100.1011
Słowa kluczowe
Wydawca
Rocznik
Tom
16
Numer
2
Strony
167-175
Opis fizyczny
Daty
wydano
2008-01-01
online
2009-03-20
Twórcy
autor
  • Gifu National College of Technology, Japan
autor
  • Hirosaki-city, Aomori, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 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. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
  • [6] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [9] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [10] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [11] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006.
  • [12] Noboru Endou, Yasunari Shidama, and Keiko Narita. Egoroff's theorem. Formalized Mathematics, 16(1):57-63, 2008.
  • [13] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.
  • [14] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
  • [15] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions. Formalized Mathematics, 9(3):525-529, 2001.
  • [16] P. R. Halmos. Measure Theory. Springer-Verlag, 1987.
  • [17] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
  • [18] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  • [19] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
  • [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [22] 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-008-0023-1
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