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<p>This note studies compactness properties of a number of subsets of probability measures on a class of metric spaces with respect to the weak convergence topology. Moreover, it is shown by an example that the space of probability measures on a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-compact metric spaces need not be a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-compact space, even though the converse statement is true for separable metric spaces. The results are used to solve a minimax newsvendor problem.</p>

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On compactness properties of subsets of probability measures on metric spaces

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Óscar Vega-Amaya,
  • Fernando Luque-Vásquez

摘要

This note studies compactness properties of a number of subsets of probability measures on a class of metric spaces with respect to the weak convergence topology. Moreover, it is shown by an example that the space of probability measures on a \(\sigma \) σ -compact metric spaces need not be a \(\sigma \) σ -compact space, even though the converse statement is true for separable metric spaces. The results are used to solve a minimax newsvendor problem.