Integral Functionals, Normal Integrands and Measurable Selections.

Abstract

A fundamental notion in many areas of mathematics, including optimal control, stochastic programming, and the study of partial differential equations, is that of an integral functional. By this is meant an expression of the form If(x) = integral over S of f(s,x(s))mu(DS), x is a member of X where X is a linear space of measurable functions defined on a measure space (S, A, mu) and having values in a linear space E. This paper provides a thorough treatment of the properties of such functionals in the case of E = R to the n-th power, including properties of continuity convexity and duality.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA037561

Entities

People

  • R. Tyrrell Rockafellar

Organizations

  • University of Washington

Tags

Communities of Interest

  • Counter IED
  • Counter WMD
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Banach Space
  • Calculus Of Variations
  • Convex Sets
  • Differential Equations
  • Dynamic Programming
  • Elements
  • Equations
  • Functional Analysis
  • Integrals
  • Mathematics
  • Normality
  • Partial Differential Equations
  • Sequences
  • Theorems
  • Tin
  • Topology

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space