Canad. Math. Bull. 49(2006), 536-548
Printed: Dec 2006
We prove that convex sets are measure convex and extremal sets are measure extremal
provided they are of low Borel complexity. We also present
examples showing that the positive results cannot be strengthened.
measure convex set, measure extremal set, face
46A55 - Convex sets in topological linear spaces; Choquet theory [See also 52A07]
52A07 - Convex sets in topological vector spaces [See also 46A55]