The Stone-Weierstrass approximation theorem is extended to certain unbounded sets in Cn. In particular, on a locally rectifiable arc going to infinity, each continuous function can be approximated by entire functions. AMS subject classification numbers. Primary: 32E30. Secondary: 32E25.

In this paper we continue the study of notion P -rectifiability in Carnot groups. We say that a Radon measure is h -rectifiable, for ? N , if it has positive -lower density and finite -upper almost everywhere, and, at every point, admits unique tangent up to multiples. prove Marstrand–Mattila rectifiability criterion arbitrary groups -rectifiable measures with planes admit normal complementary ...

Let E ⊂ R with H(E) < ∞, where H stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit