A differentiable structure for metric measure spaces (Q1826710)

The main goal of the present paper is the weakening of conditions considered by other authors under which a metric measure space admits a differentiable structure. It is known that, if a metric measure space satisfies the local condition of admitting a Poincaré inequality with a doubling measure, then the metric measure space satisfies the infinitesimal condition of admitting a differentiable structure. In the present paper, the local assumption of admitting a Poincaré inequality with a doubling measure is replaced by an infinitesimal assumption.