Automatic continuity of concave functions Academic Article uri icon

abstract

  • A necessary and sufficient condition is given that a semicontinuous, nonnegative, concave function on a finite dimensional closed convex set X necessarily be continuous at a point xx 0 ∈ X. Application of this criterion at all points of X yields a characterization, due to Gale, Klee and Rockafellar, of convex polyhedra in terms of continuity of their convex functions. © 1988 American Mathematical Society.

author list (cited authors)

  • Howe, R.

citation count

  • 2

publication date

  • April 1988