  Suppose X is an n-tuple of selfadjoint elements in a tracial von Neumann
algebra M. If z is a selfadjoint element in M and for some selfadjoint element
y in the von Neumann algebra generated by X $\delta_0(y, z) < \delta_0(y) +
\delta_0(z)$, then $\chi(X \cup \{z\}) = -\infty$ (here $\chi$ and $\delta_0$
denote the microstates free entropy and free entropy dimension, respectively).
In particular, if z lies in the von Neumann algebra generated by X, then
$\chi(X \cup \{z\}) = -\infty$. The statement and its proof are motivated by
geometric-measure-theoretic results on graphs of functions. A similar statement
for the nonmicrostates free entropy is obtained under the much stronger
hypothesis that z lies in the algebra generated by X.
