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<p>We construct a measure which determines a two variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also study the properties and behavior of such generalized means that are obtained by a measure, and we provide some applications as well.</p>

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Measures by means, means by measures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月28日

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  • Attila Losonczi

摘要

We construct a measure which determines a two variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also study the properties and behavior of such generalized means that are obtained by a measure, and we provide some applications as well.