location:  Publications → journals → CMB
Abstract view

Measure Convex and Measure Extremal Sets

Published:2006-12-01
Printed: Dec 2006
• Petr Dostál
• Jaroslav Lukeš
• Jiří Spurný
 Format: HTML LaTeX MathJax PDF PostScript

Abstract

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.
 Keywords: measure convex set, measure extremal set, face
 MSC Classifications: 46A55 - Convex sets in topological linear spaces; Choquet theory [See also 52A07] 52A07 - Convex sets in topological vector spaces [See also 46A55]