Structure of null sets in the plane and applications

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On the volume measure of non-smooth spaces with Ricci curvature bounded below (2016, background): “Preiss [1] in two dimension and recently by G.”
On the structure of A-free measures and applications (2016, background): “As already mentioned above, in [1] Alberti solved a conjecture of Ambrosio & De Giorgi [10] by showing the rank-one property for the singular part of the gradients of BV-functions (also see [2, 15]).”
On a conjecture of Cheeger (2016, result): “Note that by the same arguments of this paper Cheeger’s conjecture would also follow from the results announced in [ACP05] and [Jon11].”
On the differentiability of Lipschitz functions with respect to measures in the Euclidean space (2014, background): “Max-Planck-Institut für Mathematik in den Naturwissenschaften Inselstrasse 22, 04103 Leipzig, Germany e-mail: andrea.marchese@mis.mpg.de”