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2012 | 20 | 4 | 349-357
Tytuł artykułu

On L1Space Formed by Complex-Valued Partial Functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, we formalized L1 space formed by complexvalued partial functions [11], [15]. The real-valued case was formalized in [22] and this article is its generalization.
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
4
Strony
349-357
Opis fizyczny
Daty
wydano
2012-12-01
online
2013-02-02
Twórcy
  • 3-21-6 Suginami Tokyo, Japan
autor
  • Gifu National College of Technology, Japan
  • Shinshu University Nagano, Japan
Bibliografia
  • [1] Jonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. FormalizedMathematics, 9(3):565-582, 2001.
  • [2] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.
  • [3] Józef Białas. The _-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.
  • [4] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [5] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [8] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [10] Noboru Endou. Complex linear space and complex normed space. Formalized Mathematics, 12(2):93-102, 2004.
  • [11] P. R. Halmos. Measure Theory. Springer-Verlag, 1974.
  • [12] 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.
  • [13] Keiko Narita, Noboru Endou, and Yasunari Shidama. Integral of complex-valued measurable function. Formalized Mathematics, 16(4):319-324, 2008, doi:10.2478/v10037-008-0039-6.[Crossref]
  • [14] Andrzej Nedzusiak. _-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
  • [15] Walter Rudin. Real and Complex Analysis. Mc Graw-Hill, Inc., 1974.
  • [16] Yasunari Shidama and Noboru Endou. Integral of real-valued measurable function. FormalizedMathematics, 14(4):143-152, 2006, doi:10.2478/v10037-006-0018-8.[Crossref]
  • [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [18] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  • [19] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.
  • [20] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [22] Yasushige Watase, Noboru Endou, and Yasunari Shidama. On L1 space formed by real-valued partial functions. Formalized Mathematics, 16(4):361-369, 2008, doi:10.2478/v10037-008-0044-9.[Crossref]
  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0039-4
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