We introduce a relative fixed point property for subgroups of a locally
compact group, which we call relative amenability. It is a priori weaker than
amenability. We establish equivalent conditions, related among others to a
problem studied by Reiter in 1968. We record a solution to Reiter's problem.
We study the class X of groups in which relative amenability is equivalent to
amenability for all closed subgroups; we prove that X contains all familiar
groups. Actually, no group is known to lie outside X.
Since relative amenability is closed under Chabauty limits, it follows that
any Chabauty limit of amenable subgroups remains amenable if the ambient group
belongs to the vast class X.Comment: We added a solution to Reiter's problem and a discussion of
L^1-equivarianc
