On L¹Space Formed by Complex-Valued Partial Functions

• Autorzy: Yasushige Watase , Noboru Endou , Yasunari Shidama
• 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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2012
• Tom: 20
• Numer: 4
• Strony: 349-357

Daty

wydano

2012-12-01

online

2013-02-02

Twórcy

autor

Yasushige Watase

• 3-21-6 Suginami Tokyo, Japan

autor

Noboru Endou

• Gifu National College of Technology, Japan

autor

Yasunari Shidama

• 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.

Identyfikatory

DOI

10.2478/v10037-012-0039-4