countably compact (measure)

Definition

• Let (X,S,m) be a measure space. Then m is said to be countably compact, if there exist a countably compact subfamily of S with respect to which m is inner regular. A family of sets K is said to be countably compact, if every sequence in K with the finite intersection property has nonempty intersection.

Remark

• Every countably compact measure is perfect.

Reference

• Piotr Borodulin-Nadzieja and Grzegorz Plebanek, On compactness of mesures on Polish spaces, Illinois J. Math. Volume 49, Number 2 (2005), 531-545. http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ijm/1258138033