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2006 | 14 | 2 | 53-70
Tytuł artykułu

Integral of Measurable Function1

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we construct integral of measurable function.
Słowa kluczowe
Wydawca
Rocznik
Tom
14
Numer
2
Strony
53-70
Opis fizyczny
Daty
wydano
2006-01-01
online
2008-06-09
Twórcy
autor
  • Gifu National College of Technology, Gifu, 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 Białcs. 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] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.
  • [7] Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.
  • [8] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
  • [9] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [10] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [11] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [12] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [13] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [14] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.
  • [15] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
  • [16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions. Formalized Mathematics, 9(3):525-529, 2001.
  • [17] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Some properties of extended real numbers operations: abs, min and max. Formalized Mathematics, 9(3):511-516, 2001.
  • [18] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • [19] Grigory E. Ivanov. Definition of convex function and Jensen's inequality. Formalized Mathematics, 11(4):349-354, 2003.
  • [20] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.
  • [21] Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.
  • [22] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  • [23] Andrzej Nedzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.
  • [24] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
  • [25] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
  • [26] Yasunari Shidama and Noboru Endou. Lebesgue integral of simple valued function. Formalized Mathematics, 13(1):67-71, 2005.
  • [27] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [28] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [29] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [30] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  • [31] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [32] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [33] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [34] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-006-0008-x
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