On the existence of bounded continuous solution of Hammerstein integral equation
Azzeddine Bellour (2011)
Matematički Vesnik
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Displaying similar documents to “An inequality for the Lebesgue measure and its further applications”
On the existence of bounded continuous solution of Hammerstein integral equation
Fatou's Lemma and the Lebesgue's Convergence Theorem
Noboru Endou, Keiko Narita, Yasunari Shidama (2008)
Formalized Mathematics
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In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015
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Panchapagesan, T.V. (1995)
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The fundamental theorem of calculus for Lebesgue integral.
Bárcenas, Diómedes (2000)
Divulgaciones Matemáticas
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Exceptional directions for Sierpiński's nonmeasurable sets
B. Kirchheim, Tomasz Natkaniec (1992)
Fundamenta Mathematicae
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In [2] the question was considered in how many directions can a nonmeasurable plane set behave even "better" than the classical one constructed by Sierpiński in [6], in the sense that any line in a given direction intersects the set in at most one point. We considerably improve these results and give a much sharper estimate for the size of the sets of those "better" directions.
The general Fubini theorem in complete bornological locally convex spaces.
Haluška, Ján, Hutník, Ondrej (2010)
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Integral of Complex-Valued Measurable Function
Keiko Narita, Noboru Endou, Yasunari Shidama (2008)
Formalized Mathematics
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In this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valued measurable functions is considered.MML identifier: MESFUN6C, version: 7.9.01 4.101.1015 ...
On L p Space Formed by Real-Valued Partial Functions
Yasushige Watase, Noboru Endou, Yasunari Shidama (2010)
Formalized Mathematics
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This article is the continuation of [31]. We define the set of Lp integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that Lp integrable functions form the Lp space. We also prove Minkowski's inequality, Hölder's inequality and that Lp space is Banach space ([15], [27]).
Convergence with respect to -supported ideals
Jacek Hejduk (1997)
Colloquium Mathematicae
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Lebesgue's Convergence Theorem of Complex-Valued Function
Keiko Narita, Noboru Endou, Yasunari Shidama (2009)
Formalized Mathematics
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In this article, we formalized Lebesgue's Convergence theorem of complex-valued function. We proved Lebesgue's Convergence Theorem of realvalued function using the theorem of extensional real-valued function. Then applying the former theorem to real part and imaginary part of complex-valued functional sequences, we proved Lebesgue's Convergence Theorem of complex-valued function. We also defined partial sums of real-valued functional sequences and complex-valued functional sequences...