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<p>In this paper, we present full characterizations of a multifunction <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_904_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="111" /> </InlineMediaObject> <EquationSource Format="TEX">\(F: \Omega \rightarrow ck(X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>:</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">→</mo> <mi>c</mi> <mi>k</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> admitting a measurable by seminorm selector, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_904_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\((\Omega , \Sigma , \mu )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo>,</mo> <mi mathvariant="normal">Σ</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is a complete finite measure space and <i>ck</i>(<i>X</i>) is the family of all convex compact nonempty subsets of a Fréchet space <i>X</i>.</p>

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Characterizations of multifunctions admitting measurable by seminorm selectors

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Sokol Bush Kaliaj

摘要

In this paper, we present full characterizations of a multifunction \(F: \Omega \rightarrow ck(X)\) F : Ω → c k ( X ) admitting a measurable by seminorm selector, where \((\Omega , \Sigma , \mu )\) ( Ω , Σ , μ ) is a complete finite measure space and ck(X) is the family of all convex compact nonempty subsets of a Fréchet space X.