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Let X be an arbitrary set. A simple function on X is a real-valued function ϕ: X → ℝ with a finite range (i.e., a function that takes on only a finite number of distinct values). It is clear that ϕ is a simple function if and only if it can be represented as a linear combination of characteristic functions,

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Integral of Nonnegative Functions

  • 章节

  • 发表日期：

    2026年

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  • Carlos S. Kubrusly

摘要

Let X be an arbitrary set. A simple function on X is a real-valued function ϕ: X → ℝ with a finite range (i.e., a function that takes on only a finite number of distinct values). It is clear that ϕ is a simple function if and only if it can be represented as a linear combination of characteristic functions,