A note on compact and σ-compact subsets of probability measures on metric spaces with an application to the distribution free newsvendor problem

2023/07/13 by Vega-Amaya, Óscar, Luque-Vásquez, Fernando
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.07041

Abstract

This note identifies compact and σ-compact 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 σ-compact metric spaces not need to be σ-compact space, even though the converse statement holds true for metric spaces. The results are applied to an extended form of the distribution free newsvendor problem.

Related

• On metrisation of the space of idempotent probability measures
• Convergence in distribution of random metric measure spaces: (Lambda-coalescent measure trees)
• Point distributions in compact metric spaces, II
• Point distributions in compact metric spaces
• Markov chains and mappings of distributions on compact spaces II: Numerics and Conjectures