  We employ the ergodic theoretic machinery of scenery flows to address
classical geometric measure theoretic problems on Euclidean spaces. Our main
results include a sharp version of the conical density theorem, which we show
to be closely linked to rectifiability. Moreover, we show that the dimension
theory of measure-theoretical porosity can be reduced back to its set-theoretic
version, that Hausdorff and packing dimensions yield the same maximal dimension
for porous and even mean porous measures, and that extremal measures exist and
can be chosen to satisfy a generalized notion of self-similarity. These are
sharp general formulations of phenomena that had been earlier found to hold in
a number of special cases.
