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<p>Very often, in Mathematics, we are dealing with objects which are decomposed into simpler objects. In this paper, we introduce the concept of “multiplicative characteristic function” on arbitrary set <i>X</i> and we give a general representation theorem of any function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f:X\rightarrow [0,1]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> as a uniform limit of finite products of such type of functions. This result may be fruitfully used in measure theory, distribution theory and so on. Some consequences in uniform approximation of continuous functions are presented here.</p>

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Multiplicative Characteristic Functions: Calculus and Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月22日

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  • Ileana Bucur

摘要

Very often, in Mathematics, we are dealing with objects which are decomposed into simpler objects. In this paper, we introduce the concept of “multiplicative characteristic function” on arbitrary set X and we give a general representation theorem of any function \(f:X\rightarrow [0,1]\) f : X → [ 0 , 1 ] as a uniform limit of finite products of such type of functions. This result may be fruitfully used in measure theory, distribution theory and so on. Some consequences in uniform approximation of continuous functions are presented here.