Analysis on metric spaces emerged in the 1990s as an independent research field providing
a unified treatment of first-order analysis in diverse and potentially nonsmooth settings …

We prove that, given an $ RCD^{*}(K, N) $-space $(X, d, m) $, then it is possible to $ m $-
essentially cover $ X $ by measurable subsets $(R_ {i}) _ {i\in\mathbb {N}} $ with the …

We prove the equivalence of two seemingly very different ways of generalising
Rademacher's theorem to metric measure spaces. One such generalisation is based upon …

We represent minimal upper gradients of Newtonian functions, in the range $1\le p<\infty $,
by maximal directional derivatives along" generic" curves passing through a given point …

arXiv:1108.1324v1 [math.MG] 5 Aug 2011 Page 1 arXiv:1108.1324v1 [math.MG] 5 Aug 2011
DIFFERENTIABLE STRUCTURES ON METRIC MEASURE SPACES: A PRIMER BRUCE …

We relate generalized Lebesgue decompositions of measures in terms of curve fragments
(“Alberti representations”) and Weaver derivations. This correspondence leads to a …

We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14,
27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip …

This expository article is devoted to a survey of existent results concerning the measurable
Riemannian structure on the Sierpinski gasket and to a brief account of the author's recent …

We characterize complete RNP-differentiability spaces as those spaces which are rectifiable
in terms of doubling metric measure spaces satisfying some local (1, p)-Poincaré …

We demonstrate the necessity of a Poincaré type inequality for those metric measure spaces
that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz functions …