  We prove that the packing dimension of any mean porous Radon measure on
$\mathbb R^d$ may be estimated from above by a function which depends on mean
porosity. The upper bound tends to $d-1$ as mean porosity tends to its maximum
value. This result was stated in \cite{BS}, and in a weaker form in \cite{JJ1},
but the proofs are not correct. Quite surprisingly, it turns out that mean
porous measures are not necessarily approximable by mean porous sets. We verify
this by constructing an example of a mean porous measure $\mu$ on $\mathbb R$
such that $\mu(A)=0$ for all mean porous sets $A\subset\mathbb R$.
