Let be a unital, simple C*-algebra of stable rank one. Does there exist a commutative sub-C*-algebra
such that for every lower-semicontinuous function
there exists an open subset
such that
for
? Here,
denotes the Choquet simplex of normalized
-quasitraces on
(if
is exact, then this is just the Choquet simplex of tracial states on
), and
denotes the probability measure on
induced by the restriction of
to
.
More specifically, one may ask if this is always the case for a Cartan subalgebra of .