outer regular (i.e. can be approximated from outside by measure on the open sets) on all Borel sets, and
inner regular (i.e. can be approximated from inside by a measure on compact sets) on open sets.
If a Radon measure is -finite then it is regular (i.e. both inner and outer regular) on all Borel subsets. Left (right) Haar measure on a locally compact topological group is a nonzero Radon measure which is invariant under left (right) multiplications by elements in the group.
Literature and related entries
Gerald B. Folland, A course in abstract harmonic analysis, Studies in Adv. Math. CRC Press 1995
Revised on April 18, 2012 16:38:41
by Toby Bartels