Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1986-06-30
On the Convergence of Measurable Selections and an Application to Approximations in Stochastic OptimizationWerner Römisch (1) Humboldt-Universität zu Berlin, Germany
Conditions are given that guarantee that a sequence (of sets) of measurable selections converges almost surely, in probability and in mean. These conditions are related to the convergence of the underlying sequence of measurable multifunctions. The results are applied to approximations for the so-called "distribution problem" of stochastic optimization.
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Römisch Werner: On the Convergence of Measurable Selections and an Application to Approximations in Stochastic Optimization. Z. Anal. Anwend. 5 (1986), 277-288. doi: 10.4171/ZAA/199