*Published Paper*

**Inserted:** 5 aug 2003

**Last Updated:** 20 jan 2006

**Journal:** Real Anal. Exchange

**Volume:** 29

**Number:** 2

**Pages:** 687-712

**Year:** 2004

**Abstract:**

The graph of a function $f$ is subjected to non-homogeneous dilatations around the point $(x_0;f(x_0))$, related to the Taylor's expansion of $f$ at $x_0$. Some questions about convergence are considered. In particular the dilatated images of the graph are proved to behave nicely with respect to a certain varifold-like convergence. Further and stronger results are shown to hold in such a context, by suitably reinforcing the assumptions.

**Keywords:**
Rectifiable sets, non-homogeneous blow-up, Taylor formula