  We prove that for a typical Radon measure mu in R^d, every non-zero Radon
measure is a tangent measure of mu at mu almost every point. This was already
shown by T. O'Neil in his PhD thesis from 1994, but we provide a different
self-contained proof for this fact. Moreover, we show that this result is
sharp: for any non-zero measure we construct a point in its support where the
set of tangent measures does not contain all non-zero measures. We also study a
concept similar to tangent measures on trees, micromeasures, and show an
analogous typical property for them.
