Some Characteristics of the Process Measure of the Amount of Information
Branislav D. Vidaković (1983)
Publications de l'Institut Mathématique
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Branislav D. Vidaković (1983)
Publications de l'Institut Mathématique
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G. Fodor (1951)
Compositio Mathematica
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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.
Marcin E. Kuczma (1976)
Colloquium Mathematicae
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Allan Joseph Champneys Cunningham
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Robert Morris Pierce
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Goertzel, Ben (1992)
International Journal of Mathematics and Mathematical Sciences
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Robert E. Zink (1966)
Colloquium Mathematicae
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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.
James Fickett, Jan Mycielski (1979)
Colloquium Mathematicae
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Noboru Endou (2015)
Formalized Mathematics
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In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore,...