Integrals, conditional expectations, and martingales of multivalued functions

Hiai, Fumio; Umegaki, Hisaharu

doi:10.1016/0047-259x(77)90037-9

Cited by 632 publications

(287 citation statements)

References 17 publications

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“…Recall that a subset K of L l [Q,R") is said to be decomposable ( [9]) if for every u, veK and Ae£f we have UX A + VXQ\AGK> where XA stands for the characteristic function of A. We denote by 3) the family of all decomposable closed nonempty subsets of Note that the function v(.,.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On a non-convex hyperbolic differential inclusion

Staicu

1992

Proceedings of the Edinburgh Mathematical Society

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Section: Introduction and Main Resultsmentioning

confidence: 99%

On a non-convex hyperbolic differential inclusion

Staicu

1992

Proceedings of the Edinburgh Mathematical Society

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“…Different definitions of measurability for set-valued functions are developed over the years by several authors (cf. [4,13,23,24] and reference therein).…”

Section: Preliminary Resultsmentioning

confidence: 99%

Integration in a dynamical stochastic geometric framework

Aletti¹,

Bongiorno²,

Capasso³

2011

ESAIM: PS

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Abstract. Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary regularities arising from an analytical definition of the front growth. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, is non local, i.e. at a fixed time instant, growth is the same at each point of the space.Mathematics Subject Classification. 60D05, 53C65, 60G20.

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“…We will start with an auxilliary result that we will need in what follows and which also generallzes Theorem 1.5 of Hlai-Umegakl [9]. …”

Section: Properties Of the Set Of Integrable Selectorsmentioning

confidence: 99%

Measurable multifunctions and their applications to convex integral functionals

Papageorgiou

1988

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. The purpose of this paper is to establlsh some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functlonals defined on Lebesgue-Bochner spaces. In this processwe also obtain a characterization of separable dual Banach spaces using multlfunctlons and we present some generalizations of the classical "bang-bang" principle to infinite dimensional linear control systems with time dependent control constraints.

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Integrals, conditional expectations, and martingales of multivalued functions

Cited by 632 publications

References 17 publications

On a non-convex hyperbolic differential inclusion

On a non-convex hyperbolic differential inclusion

Integration in a dynamical stochastic geometric framework

Measurable multifunctions and their applications to convex integral functionals

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