• Corpus ID: 246016413

# Random sets and Choquet-type representations

```@inproceedings{Ararat2022RandomSA,
title={Random sets and Choquet-type representations},
author={cCaugin Ararat and Umur Cetin},
year={2022}
}```
• Published 16 January 2022
• Mathematics
As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, Choquet decompositions and Choquet convex decompositions, as well as their corresponding hull operators acting on the power sets of LebesgueBochner spaces. We show that Choquet hull coincides with convex hull in the finite-dimensional setting, yet Choquet hull tends to be larger in infinite dimensions. We also provide a quantitative characterization of Choquet hull…

## References

SHOWING 1-10 OF 16 REFERENCES
Lectures on Choquet's Theorem
Preface.- Introduction. The Krein-Milman theorem as an integral representation theorem.- Application of the Krein-Milman theorem to completely monotonic functions.- Choquet's theorem: The metrizable
Convexity: An Analytic Viewpoint
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions
The Radon-Nikodym theorem for the Bochner integral
Main Theorem. Let (X, S, p) be a o-finite positive measure space and let B be a Banach space. Let m be a B-valued measure on S. Then m is the indefinite integral with respect to p of a B-valued
Theory of Random Sets
Random Closed Sets and Capacity Functionals.- Expectations of Random Sets.- Minkowski Addition.- Unions of Random Sets.- Random Sets and Random Functions.
Functional Analysis
A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with
Probability and Stochastics
Preface.- Measure and Integration.- Probability Spaces.- Convergence.- Conditioning.- Martingales and Stochastics.- Poisson Random Measures.- Levy Processes.- Index.- Bibliography
) and Corollary 7.12, we have chcd s chcd p A = chd s conv chd p conv A = chd s chd p conv A = chd s conv A = chcd s A