On the theory of Banach space valued multifunctions. I: Integration and conditional expectation

DOI10.1016/0047-259X(85)90078-8zbMath0579.28009OpenAlexW2050419975MaRDI QIDQ1067034

Nikolaos S. Papageorgiou

Publication date: 1985

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(85)90078-8

zbMATH Keywords

Hausdorff metricJames' theoremRadon-Nikodým propertymeasurable selectionAumann integral of Banach space valued multifunctionsset- valued conditional expectation

Mathematics Subject Classification ID

Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10)

Related Items

A stability result for differential inclusions in Banach spaces, A convergence theorem of fuzzy-valued martingales in the extended Hausdorff metric \(\mathbf {H}_{\infty}\), Doob's Decomposition Theorem for Fuzzy (Super) Submartingales, Approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions, Relation between relaxability and performance stability for optimal control problems governed by non-linear evolution equations, An Inexact Bundle Method and Subgradient Computations for Optimal Control of Deterministic and Stochastic Obstacle Problems, On the existence of solutions for random differential inclusions in a Banach space, Carathéodory solutions of fuzzy differential equations, On the attainable set of differential inclusions and control systems, Optimization of controlled evolution equations under indeterminacy conditions, A continuous version of the relaxation theorem for nonlinear evolution inclusions, Stochastic Nash equilibrium problems: sample average approximation and applications, A necessary extremality condition for a set-valued stochastic control problem, On the Theory of (Dual) Projection for Fuzzy Stochastic Processes, Random fuzzy number integrals in Banach spaces, Random fuzzy sets and fuzzy martingales, Fuzzy valued measure, On bounded solutions of differential inclusions in Banach spaces, Controllability of impulsive evolution inclusions with nonlocal conditions, The oscillation of delay differential inclusions and fuzzy biodynamics models, Fuzzy integrals of set-valued mappings and fuzzy mappings, Convergence theorems for set-valued amarts and uniform amarts, On the properties of the Aumann integral with applications to differential inclusions and control systems, Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces, Approximation of fuzzy integrals using fuzzy Bernstein polynomials, On nonconvex valued Volterra integral inclusions in Banach spaces, Nonsmooth analysis and approximation, Optimal control of nonlinear evolution inclusions, Convergence analysis of stationary points in sample average approximation of stochastic programs with second order stochastic dominance constraints, A note on uniform exponential convergence of sample average approximation of random functions, On the optimal control and relaxation of nonlinear infinite dimensional systems, On infinite-dimensional control systems with state and control constraints, An existence theorem for an optimal control problem in banach spaces, A convergence theorem for set valued supermartingales with values in a separable banach space^∗, Fuzzy martingales - a simple form of fuzzy processes^∗, New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations, Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions, A new integral with respect to a generalized fuzzy number measure, A GENERAL METHOD FOR CONVERGENCE THEOREMS OF FUZZY SET-VALUED RANDOM VARIABLES AND ITS APPLICATIONS TO MARTINGALES AND UNIFORM AMARTS, On the solution set of differential inclusions in Banach space, Approximating stationary points of stochastic optimization problems in Banach space, New set-valued integral in a Banach space, Nonlinear Volterra integrodifferential evolution inclusions and optimal control, Weak convergence of random sets in Banach spaces, On multivalued supermartingales with continuous parameter:martingale selectors and their regularity, Asymptotic analysis of sample average approximation for stochastic optimization problems with joint chance constraints via conditional value at risk and difference of convex functions, On Convergence and Closedness of Multivalued Martingales, On representation and regularity of continuous parameter multivalued martingales, Solutions of evolution inclusions. I, Set valued Bartle integrals, Decomposition and representation theorem of set-valued amarts, On the Conditional Expectation and Convergence Properties of Random Sets, Oscillation property for fuzzy delay differential equations, On the dependence of the solutions and optimal solutions of control problems on the control constraint set, On the dependence of the solutions and optimal solutions of control problems on the control constraint set, Properties of the trajectories of set-valued integrals in banach spaces, Regularity and stopping theorem for fuzzy martingales with continuous parameters, On Fatou's lemma and parametric integrals for set-valued functions, Uniform exponential convergence of sample average random functions under general sampling with applications in stochastic programming, Transition vector measures and multimeasures and parametric set-valued integrals, Controllability of evolution inclusions with nonlocal conditions, Two-stage stochastic equilibrium problems with equilibrium constraints: modeling and numerical schemes, On the comparison of Aumann and Bochner integrals, Representation of Set Valued Operators, Gaussian processes and martingales for fuzzy valued random variables with continuous parameter, Transition vector measures and multimeasures and parametric set-valued integrals, Stochastic integral with respect to set-valued square integrable martingales, Optional and predictable projections of set-valued measurable processes, Essential (convex) closure of a family of random sets and its applications, Weak Convergence and Weak Compactness for Multifunctions with Values in a Separable Banach Space, Solutions of Cauchy and periodic problems for evolution inclusions with multi-valued \(w_{\lambda_0}\)-pseudomonotone maps, Unnamed Item, On the existence of impulsive neutral evolution differential inclusions with infinite delay, Parametrized relaxation for evolution inclusions of the subdifferential type, On the bang-bang principle for nonlinear evolution inclusions, On integral inclusions of Volterra type in Banach spaces, Contributions to the Theory of Set Valued Functions and Set Valued Measures, Convergence and representation theorems for set valued random processes, Convergence theorems for set-valued martingales and semimartingales, Random differential inclusions in Banach spaces, Convergence and representation theorems for set valued random processes, Integrals of fuzzy-number-valued functions, Relaxation and existence of optimal controls of systems governed by evolution inclusions in separable Banach spaces, Approximate controllability for impulsive Riemann-Liouville fractional differential inclusions, Infinite Horizon Optimal Control Problems for Semilinear Evolution Equations, Some properties and convergence theorems for fuzzy-valued Kluvánek-Lewis integrals, On retarded fuzzy functional differential equations and nonabsolute fuzzy integrals, Convergence of set-valued and fuzzy-valued martingales, On the convergence and representation of random fuzzy number integrals, Fubini theorem for generalized fuzzy number-valued integrals, Stochastic integrals of set-valued processes and fuzzy processes, Convergence of set valued sub- and supermartingales in the Kuratowski-Mosco sense, Fuzzy integrals for set-valued mappings, Radon-Nikodym theorem and Vitali-Hahn-Saks theorem on fuzzy number measures in Banach spacers, Fuzzy conditional expectation, On the structure of solutions for fuzzy initial value problem, The integral theory of Ioffe's fans

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On conditional expectation of random sets
• Convex analysis and measurable multifunctions
• An elementary proof that integration preserves uppersemicontinuity
• On the relations between two types of convergence for convex functions
• Integrals, conditional expectations, and martingales of multivalued functions
• Radon-Nikodym theorems for set-valued measures
• p-integrale selectors of multimeasures
• Integrals of set-valued functions
• Multi-applications mesurables à valeurs convexes compactes
• Measurable dependence of convex sets and functions on parameters
• Measurable relations
• Weak Sequential Convergence in L ∞ E and Dunford-Pettis Property of L 1 E
• The Existence of Probability Measures with Given Marginals
• Fatou's Lemma in Several Dimensions
• Set-Valued Measures