Journal Article10.1007/BF01168566
Measurable selection theorems for optimization problems
81
TL;DR: In this article, the authors attempt a unification of several selection theorems in the literature by introducing the notion of a selection class and give sufficient conditions for the existence of measurable e-maximizers.
read more
Abstract: In this paper we attempt a unification of several selection theorems in the literature by introducing the notion of a selection class and give sufficient conditions for the existence of measurable e-maximizers. Various special cases are discussed. Finally, as an application of the selection theorem of Kuratowski and Ryll-Nardzewski [12] a Baire classification of e-maximizers is determined.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Discrete-time controlled Markov processes with average cost criterion: a survey
Aristotle Arapostathis,Vivek S. Borkar,E. Fernandez-Gaucherand,Mrinal K. Ghosh,Steven I. Marcus +4 more
TL;DR: A survey of the average cost control problem for discrete-time Markov processes can be found in this paper, where the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades.
•Posted Content
E-values: Calibration, combination, and applications
Vladimir Vovk,Ruodu Wang +1 more
TL;DR: It is demonstrated that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e- Values can be merged simply by averaging them, which allows to develop efficient procedures using e- values for testing multiple hypotheses.
106
E-values: Calibration, combination and applications
Vladimir Vovk,Ruodu Wang +1 more
TL;DR: It is demonstrated that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e- Values can be merged simply by averaging them, which allows to develop efficient procedures using e- values for testing multiple hypotheses.
102
Average cost Markov control processes with weighted norms: existence of canonical policies
TL;DR: In this article, the authors considered discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion.
On the Existence of Nash Equilibrium in Bayesian Games
TL;DR: By allowing for payoff discontinuities in actions, this work covers various applications that cannot be handled by extant results and assures the existence of a Bayes-Nash equilibrium.
References
Survey of Measurable Selection Theorems
TL;DR: In this article, Kuratowski and Ryll-Nardzewski showed that the existence off problem can be solved by lifting F in a natural way to a map into the closed sets of a Polish space.
610
Measurable Selections of Extrema
Lawrence D. Brown,R. Purves +1 more
TL;DR: In this article, the existence of a Borel measurable Bayes procedure was shown to be a non-trivial problem, and a counterexample was given in which such a measure fails to exist.
236
The Optimal Reward Operator in Dynamic Programming
TL;DR: In this article, the authors consider a dynamic programming problem with analytic state space, analytic constraint set, and semi-analytic reward function, and show that the optimal reward in one move is $T^n0, a semi-optimistic function on the analytic state set.
Related Papers (5)
Onésimo Hernández-Lerma
- 01 May 1989
Onésimo Hernández-Lerma,Jean B. Lasserre +1 more
- 22 Jun 1999
E. B. Dynkin,A. A. I︠U︡shkevich,J. M. Danskin,C. Holland +3 more
- 01 Jan 1965
Dimitri P. Bertsekas,Steven E. Shreve +1 more
- 01 Feb 2007