*Definition [#t86717d9]
A compact Hausdorff space X is said to be Radon-Nikodym compact if there exists a lower semicontinuous metric with the following property: For every nonempty subset A of X and every positive number ε, there exists an open set U which meets A with radius less than ε.

*Remark [#rdfc80a4]
-It is also called [[RN compact]]

*Reference [#f35273cf]
Klaas Pieter Hart, Jun-iti Nagata and Jerry E. Vaughan, ''Encyclopedia of general topology'', Elsevier Science Publishers, B.V., Amsterdam, 2004.