Displaying similar documents to “On differentiation of Lebesgue double integrals”

On the linear Denjoy property of two-variable continuous functions

Miklós Laczkovich, Ákos K. Matszangosz (2015)

Colloquium Mathematicae

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The classical Denjoy-Young-Saks theorem gives a relation, here termed the Denjoy property, between the Dini derivatives of an arbitrary one-variable function that holds almost everywhere. Concerning the possible generalizations to higher dimensions, A. S. Besicovitch proved the following: there exists a continuous function of two variables such that at each point of a set of positive measure there exist continuum many directions, in each of which one Dini derivative is infinite...

The Hausdorff lower semicontinuous envelope of the length in the plane

Raphaël Cerf (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the Hausdorff lower semicontinuous envelope of the length in the plane. This envelope is taken with respect to the Hausdorff metric on the space of the continua. The resulting quantity appeared naturally as the rate function of a large deviation principle in a statistical mechanics context and seems to deserve further analysis. We provide basic simple results which parallel those available for the perimeter of Caccioppoli and De Giorgi.