Displaying similar documents to “Hereditary measurable sets and universal measure”

Construction of Measure from Semialgebra of Sets1

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,...

On the uniform limit of quasi-continuous functions.

Baltasar Rodríguez-Salinas (2001)

RACSAM

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Estudiamos cuando el límite uniforme de una red de funciones cuasi-continuas con valores en un espacio localmente convexo X es también una función cuasi-continua, resaltando que esta propiedad depende del menor cardinal de un sistema fundamental de entornos de O en X, y estableciendo condiciones necesarias y suficientes. El principal resultado de este trabajo es el Teorema 15, en el que los resultados de [7] y [10] son mejorados, en relación al Teorema de L. Schwartz.

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.

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.

Big set of measure zero

Ladislav Mišík (2001)

Acta Mathematica et Informatica Universitatis Ostraviensis

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