Displaying similar documents to “Carleson embeddings.”

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.

Conical measures and properties of a vector measure determined by its range

L. Rodríguez-Piazza, M. Romero-Moreno (1997)

Studia Mathematica

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We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...

On the extension of measures.

Baltasar Rodríguez-Salinas (2001)

RACSAM

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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.