Study of lipschitz functions over metric measure spaces

Abstract

The motive of this thesis is to review generalization of characteristic of lipschitz function over metric measure spaces. We also review the results in the class of metric-measure spaces which satisfy version(strong) of doubling condition(Bishop-Gromov regularity)[10].In fact, we set up a necessary and su cient condition in the direction that any measurable function that assure integrability condition is to be essentially Lipschitzian. As well as we review the generalized version of di erentiability property (having derivative zero) of functions [14] and [13], after that we review about the characterization of constant function [1]