Mahler measure of the Horie unit and Weber's class number problem in the cyclotomic ℤ₃-extension of ℚ
Takayuki Morisawa (2012)
Acta Arithmetica
Similarity:
Takayuki Morisawa (2012)
Acta Arithmetica
Similarity:
Edward Dobrowolski (2006)
Acta Arithmetica
Similarity:
Charles L. Samuels (2007)
Acta Arithmetica
Similarity:
Robert Morris Pierce
Similarity:
Noboru Endou (2015)
Formalized Mathematics
Similarity:
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,...
Noboru Endou (2017)
Formalized Mathematics
Similarity:
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.
Robert E. Zink (1966)
Colloquium Mathematicae
Similarity:
Noboru Endou (2016)
Formalized Mathematics
Similarity:
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.
Edward Dobrowolski (2012)
Acta Arithmetica
Similarity:
Karol Borsuk (1983)
Annales Polonici Mathematici
Similarity:
James Fickett, Jan Mycielski (1979)
Colloquium Mathematicae
Similarity:
Matilde N. Lalín, Jean-Sébastien Lechasseur (2016)
Acta Arithmetica
Similarity:
We prove formulas for the k-higher Mahler measure of a family of rational functions with an arbitrary number of variables. Our formulas reveal relations with multiple polylogarithms evaluated at certain roots of unity.
Dedić, Ljuban (1990)
Publications de l'Institut Mathématique. Nouvelle Série
Similarity:
T. Świątkowski (1967)
Colloquium Mathematicae
Similarity:
S. N. Mukhopadhyay (1967)
Colloquium Mathematicae
Similarity:
G. Fodor (1951)
Compositio Mathematica
Similarity:
Ihor Stasyuk, Edward D. Tymchatyn (2013)
Colloquium Mathematicae
Similarity:
Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear...
John Garza (2009)
Acta Arithmetica
Similarity: