<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let <italic>(X,A,</italic>μ<italic>)</italic> be a complete probability space, ρ a lifting, <italic>T</italic>ρ the associated Hausdorff lifting topology on X and <italic>E</italic> a Banach space. Suppose <italic>F:</italic> (X,Tρ<italic>)</italic><italic>-> E”</italic>σ be a bounded continuous mapping. It is proved that there is an <italic>A</italic> ∈ <italic>A</italic> such that <italic>FXA</italic> has range in a closed separable subspace of <italic>E</italic> (so <italic>FXA:X</italic> → <italic>E</italic> is strongly measurable) and for any <italic>B</italic> ∈ <italic>A</italic> with μ<italic>(B)</italic> > 0 and B ∩ <italic>A =</italic> ø, <italic>F<sub>XB</sub></italic> cannot be weakly equivalent to a <italic>E-</italic>valued strongly measurable function. Some known results are obtained as corollaries.</p></abstract>

Let (X,A,μ) be a complete probability space, ρ a lifting, Tρ the associated Hausdorff lifting topology on X and E a Banach space. Suppose F: (X,Tρ)-> E”σ be a bounded continuous mapping. It is proved that there is an A ∈ A such that FXA has range in a closed separable subspace of E (so FXA:X → E is strongly measurable) and for any B ∈ A with μ(B) > 0 and B ∩ A = ø, FXB cannot be weakly equivalent to a E-valued strongly measurable function. Some known results are obtained as corollaries.

A decomposition of bounded, weakly measurable functions

Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U S.A.

Tatra Mountains Mathematical Publications

{"article-title":"A decomposition of bounded, weakly measurable functions"}

Let (X,A,μ) be a complete probability space, ρ a lifting, Tρ the associated Hausdorff lifting topology on X and E a Banach space. Suppose F: (X,Tρ)-> E”σ be a...

A decomposition of bounded, weakly measurable functions

Publié en ligne: 13 nov. 2012

Pages: 67 - 70

DOI: https://doi.org/10.2478/v10127-011-0025-1

Mots clés
liftings, weakly measurable functions, weakly equivalent functions, vector measures with finite variations.

This content is open access.

A decomposition of bounded, weakly measurable functions

Publié en ligne: 13 nov. 2012

Pages: 67 - 70

DOI: https://doi.org/10.2478/v10127-011-0025-1

Mots clésliftings, weakly measurable functions, weakly equivalent functions, vector measures with finite variations.

This content is open access.

Mots clés
liftings, weakly measurable functions, weakly equivalent functions, vector measures with finite variations.