The Orlicz-Kantorovich spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7743_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{\Phi }(B,m)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">Φ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>B</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> associated with the complete Boolean algebra B, the Orlicz function <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7743_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Phi $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Φ</mi> </math></EquationSource> </InlineEquation>, and the measure m given on B and taking values in the algebra of all measurable real functions are considered. It is shown that <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7743_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{\Phi }(B,m)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">Φ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>B</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is a symmetric Banach-Kantorovich space with the Fatou property.

THE ORLICZ-KANTOROVICH SYMMETRIC SPACE

期刊论文
发表日期：

2025年5月26日

查看全文

Vladimir Chilin,
Botir Zakirov

摘要

The Orlicz-Kantorovich spaces $L_{\Phi }(B,m)$ $L_{Φ} (B, m)$ associated with the complete Boolean algebra B, the Orlicz function $\Phi $ $Φ$ , and the measure m given on B and taking values in the algebra of all measurable real functions are considered. It is shown that $L_{\Phi }(B,m)$ $L_{Φ} (B, m)$ is a symmetric Banach-Kantorovich space with the Fatou property.