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Convergence of Cones of Metric Measure Spaces and Its Application to Cauchy Distribution

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A sequence of cones in metric measure spaces converges under specific topologies.
The Cauchy distribution converges to a half line in concentration topology as dimensions grow.
This convergence presents a novel case apart from Gaussian distributions.
The findings enhance our understanding of metric measure spaces and statistical distributions.

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The sequence of cones converges in metric measure spaces, suggesting new pathways to understand Cauchy distributions.

Esaki et al. (2025) studied this question.

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