<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let <italic>I </italic>⊂<italic></italic>R be an interval,(<italic>X,</italic>ℳ(<italic>X</italic>)) a measure space, and (<italic>Z, </italic>∥⋅∥) a reflexive Banach space. We prove that a multifunction <italic>F </italic>from <italic>X × I </italic>to <italic>Z</italic> is measurable whenever it is ℳ(<italic>X</italic>)-measurable in the first and approximately continuous and almost everywhere continuous in the second variable.</p></abstract>

Let I ⊂R be an interval,(X,ℳ(X)) a measure space, and (Z, ∥⋅∥) a reflexive Banach space. We prove that a multifunction F from X × I to Z is measurable whenever it is ℳ(X)-measurable in the first and approximately continuous and almost everywhere continuous in the second variable.

A note on measurability of multifunctions approximately continuous in second variable

Pomeranian Academy Institute of Mathematics Arciszewskiego 22a PL–76-200 Słupsk POLAND

Tatra Mountains Mathematical Publications

Let I ⊂R be an interval,(X,ℳ(X)) a measure space, and (Z, ∥⋅∥) a reflexive Banach space. We prove that a multifunction F from X × I to Z is measurable whenever...

A note on measurability of multifunctions approximately continuous in second variable

Published Online: Nov 19, 2012

Page range: 91 - 100

DOI: https://doi.org/10.2478/v10127-012-0030-z

Keywords
multifunctions, approximate continuity, integrability, measurability.

This content is open access.

A note on measurability of multifunctions approximately continuous in second variable

Published Online: Nov 19, 2012

Page range: 91 - 100

DOI: https://doi.org/10.2478/v10127-012-0030-z

Keywordsmultifunctions, approximate continuity, integrability, measurability.

This content is open access.

Keywords
multifunctions, approximate continuity, integrability, measurability.