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Fubini’s Theorem on Measure

100%

Endou N.

Formalized Mathematics

2017

tom 25

nr 1

1-29

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.

Product Pre-Measure

100%

Endou N.

Formalized Mathematics

2016

tom 24

nr 1

69-79

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.

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2 Formalized Mathematics

2 Endou N.

1 2017

1 2016

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Fubini’s Theorem on Measure

Product Pre-Measure