A note on the Denjoy integral
K. Krzyżewski (1968)
Colloquium Mathematicae
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K. Krzyżewski (1968)
Colloquium Mathematicae
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J. Musielak, W. Orlicz (1959)
Studia Mathematica
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T. Świątkowski (1967)
Colloquium Mathematicae
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M. Stojaković (1966)
Matematički Vesnik
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S. N. Mukhopadhyay (1967)
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L. Moser, M. G. Murdeshwar (1966)
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H. Światak (1965)
Annales Polonici Mathematici
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F. M. Filipczak (1964)
Colloquium Mathematicae
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W. Wojtyński (1966)
Colloquium Mathematicae
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R. Taberski (1964)
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Robert E. Zink (1966)
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Andrzej Pliś, Tadeusz Ważewski (1962)
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Noboru Endou (2016)
Formalized Mathematics
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In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.
A. I. Fine, S. Kass (1966)
Annales Polonici Mathematici
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Noboru Endou (2017)
Formalized Mathematics
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The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description. First of all, for the product measure constructed in [14], we show some theorems. Then we introduce the section which plays an important role in Fubini’s theorem, and prove the relevant proposition. Finally we show Fubini’s theorem on measure.