Nonstandard Analysis of Graphs
arXiv:math/0106003
Abstract
This paper shows certain classes of metric spaces characterized by volume growth properties of balls can viewed as graphs with infinitesimal edges. Our approach is based on nonstandard analysis.
31 pages. Added references. Corrected various errors (e.g. replaced an occurrence of "reals" with "hyperreals" and and several occurrences of the symbol for open ball with that for closed ball). Added details of some proofs