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<p>We prove that every plurifinely continuous function on an open set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega\subset \mathbb{C}^n (n\geq 1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>≥</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is quasi-continuous relatively to the Bedford-Taylor capacity on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Omega\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>.</p>

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Plurifinely continuous functions are quasi-continuous

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • M. El Kadiri

摘要

We prove that every plurifinely continuous function on an open set \(\Omega\subset \mathbb{C}^n (n\geq 1)\) Ω ⊂ C n ( n ≥ 1 ) is quasi-continuous relatively to the Bedford-Taylor capacity on \(\Omega\) Ω .