Egoroff's Theorem

• Autorzy: Noboru Endou , Yasunari Shidama , Keiko Narita
• Języki publikacji: EN

Abstrakty

EN

The goal of this article is to prove Egoroff's Theorem [13]. However, there are not enough theorems related to sequence of measurable functions in Mizar Mathematical Library. So we proved many theorems about them. At the end of this article, we showed Egoroff's theorem.MML identifier: MESFUNC8, version: 7.8.10 4.100.1011

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2008
• Tom: 16
• Numer: 1
• Strony: 57-63

Daty

wydano

2008-01-01

online

2009-03-20

Twórcy

autor

Noboru Endou

• Gifu National College of Technology, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

autor

Keiko Narita

• Hirosaki-city, Aomori, Japan

Bibliografia

• [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [2] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.
• [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
• [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] Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.
• [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [8] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [9] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006.
• [10] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.
• [11] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.
• [12] Adam Grabowski. On the Kuratowski limit operators. Formalized Mathematics, 11(4):399-409, 2003.
• [13] P. R. Halmos. Measure Theory. Springer-Verlag, 1987.
• [14] 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.
• [15] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
• [16] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
• [17] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
• [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
• [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
• [21] 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.
• [22] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Limit of sequence of subsets. Formalized Mathematics, 13(2):347-352, 2005.

Identyfikatory

DOI

10.2478/v10037-008-0009-z