I've been looking at Folner's Condition recently, and I'm struggling to find a proof for why the existence of a Folner sequence on a locally compact group implies that it is amenable (and the converse to this).

[EDIT: So far I've looked at amenability in terms of invariant means, so my question should be:

"How does to existence of a Folner sequence imply the existence of a left invariant mean on a locally compact group?"]

If anyone could give a proof for this or point me in the direction of one on the internet that I can read that would be really helpful - have struggled to find anything myself.

Thanks in advance, Jo