The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “The Relevance of Measure and Probability, and Definition of Completeness of Probability”

On the extension of measures.

Baltasar Rodríguez-Salinas (2001)

RACSAM

Similarity:

We give necessary and sufficient conditions for a totally ordered by extension family (Ω, Σ, μ) of spaces of probability to have a measure μ which is an extension of all the measures μ. As an application we study when a probability measure on Ω has an extension defined on all the subsets of Ω.

Construction of Measure from Semialgebra of Sets1

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,...

Radon measures

David H. Fremlin (2004)

Acta Universitatis Carolinae. Mathematica et Physica

Similarity:

Hopf Extension Theorem of Measure

Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama (2009)

Formalized Mathematics

Similarity:

The authors have presented some articles about Lebesgue type integration theory. In our previous articles [12, 13, 26], we assumed that some σ-additive measure existed and that a function was measurable on that measure. However the existence of such a measure is not trivial. In general, because the construction of a finite additive measure is comparatively easy, to induce a σ-additive measure a finite additive measure is used. This is known as an E. Hopf's extension theorem of measure...

Fubini’s Theorem on Measure

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.