An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems

DOI10.1007/BF02844536zbMath0606.60006MaRDI QIDQ1084738

Erik J. Balder

Publication date: 1985

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

zbMATH Keywords

semicontinuity theoremscompactness property of sets of transition probabilitiesexistence theory for optimal control

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving ordinary differential equations (49J15) Spaces of measures, convergence of measures (28A33) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

On weak convergence implying strong convergence in L₁-spaces, Young measures, weak and strong convergence and the Visintin-Balder theorem, Infinite-dimensional extension of a theorem of Komlós, Semicontinuity of an integral functional in a Banach space, Fatou's lemma in infinite dimensions, On infinite-horizon lower closure results for optimal control, Nonsmooth analysis of doubly nonlinear evolution equations, Irreversibility and alternate minimization in phase field fracture: a viscosity approach, Truncation methods applied to problems of weak or strong convergence in \(L^ 1\), Analysis of staggered evolutions for nonlinear energies in phase field fracture, Convergence of alternate minimization schemes for phase-field fracture and damage, Consistent finite-dimensional approximation of phase-field models of fracture, Gradient flows of non convex functionals in Hilbert spaces and applications, Applications of the method of compactness and decomposition: minimization, convergence of martingales, multivalued Fatou lemma, New sequential compactness results for spaces of scalarly integrable functions

Cites Work

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• On existence problems for the optimal control of certain nonlinear integral equations of Urysohn type
• An existence result for optimal economic growth problems
• Non convex control problems in Banach spaces
• Semicontinuita inferiore di un funzionale integrale dipendente da funzioni di classe \(L^ p\) a valori in uno spazio di Banach
• Continuity and compactness of measures
• Weak lower semicontinuity of integral functionals
• Infinite dimensional linear systems theory
• A variational problem arising in economics
• A General Approach to Lower Semicontinuity and Lower Closure in Optimal Control Theory
• Lower Semicontinuity of Integral Functionals with Nonconvex Integrands by Relaxation-Compactification
• Lower Closure Problems with Weak Convergence Conditions in a New Perspective
• Measurable relations
• On Lower Semicontinuity of Integral Functionals. I
• An existence theorem for pareto problems
• Intégrandes normales et mesures paramétrées en calcul des variations
• Relaxed Controls and Variational Problems