Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
Source Normalized Impact per Paper (SNIP) 2015: 0.686
Impact per Publication (IPP) 2015: 0.296

Open Access
Online
ISSN
1898-9934
See all formats and pricing
In This Section
Volume 20, Issue 4 (Dec 2012)

Issues

On L1 Space Formed by Complex-Valued Partial Functions

Yasushige Watase
  • 3-21-6 Suginami Tokyo, Japan
/ Noboru Endou
  • Gifu National College of Technology, Japan
/ Yasunari Shidama
  • Shinshu University Nagano, Japan
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0039-4

Summary

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.

  • [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.

About the article

Published Online: 2013-02-02

Published in Print: 2012-12-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0039-4. Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in