The Stepanov differentiability theorem in metric measure spaces
Balogh, Zoltán ; Rogovin, Kevin ; Zürcher, Thomas
In: The Journal of Geometric Analysis, 2004, vol. 14, no. 3, p. 405-422
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- We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As a consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequality