Displaying similar documents to “Mahler's measure of a polynomial in terms of the number of its monomials”

Irreducible polynomials with all but one zero close to the unit disk

DoYong Kwon (2016)

Colloquium Mathematicae

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We consider a certain class of polynomials whose zeros are, all with one exception, close to the closed unit disk. We demonstrate that the Mahler measure can be employed to prove irreducibility of these polynomials over ℚ.

Fubini’s Theorem on Measure

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.

Product Pre-Measure

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.