Vol. 59, No. 1, 1975

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Convex integrands on Souslin locally convex spaces

Michel Valadier

Vol. 59 (1975), No. 1, 267–276

R. T. Rockafellar has proved a formula for the conjugates of convex integral functionals on vector spaces of measurable vector-valued functions. This formula is extended to the case where the spaces of values of the measurable functions is a Souslin locally convex space. Rockafellar’s definition of decomposable space of measurable vector-valued functions is extended to other than normed spaces. In the first section technical results on measurable set-valued functions are given.

Mathematical Subject Classification 2000
Primary: 46G10
Received: 10 May 1973
Published: 1 July 1975
Michel Valadier