W. Briec, C.D. Horvath and A. Rubinov

Key words:

-convexity, gauges, co-gauges, separation,

-measurable maps

Mathematices Subject Classification: 46A22, 52A30, 06F30

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Copyright© 2005 Yokohama Publishers

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of

is

-convex if for all x 1, x 2

[0,1]

Abstract:

A subset

B and all t

one has tx 1

x 2

B. These sets were first investigated in [1] where it was shown

that Carathéodory, Radon and Helly like Theorems hold. In this work we establish

separation and Hahn-Banach like Theorems for

-convex sets.

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Special Issue in Honor of the 70th Birthday of R.Tyrrell Rockafellar
Volume 1, Number 1, January 2005, pp. 13-30