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