On locally finite-dimensional traces

We partially resolve two open questions on approximation properties of traces on simple C-*-algebras. We answer a question raised by Nate Brown by showing that locally finite-dimensional (LFD) traces form a convex set for simple C-*-algebras. We prove that all the traces on the reduced C-*-algebra C-r(*)(G) of a discrete amenable ICC group G are LFD, and conclude that C-r(*)(G) is strong-NF in the sense of Blackadar-Kirchberg in this case. This partially answers another open question raised by Brown.