Inserted: 6 apr 2004
Last Updated: 8 dec 2004
Journal: Journal of Geometric Analysis
We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequality.
Keywords: Stepanov differentiability , doubling measure, differentiable structure, Poincare inequality