Displaying similar documents to “On the connection between Hausdorff measures and generalized capacity”

Negligible sets and good functions on polydiscs

Kohur Gowrisankaran (1979)

Annales de l'institut Fourier

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A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.

Research Article. Multiscale Analysis of 1-rectifiable Measures II: Characterizations

Matthew Badger, Raanan Schul (2017)

Analysis and Geometry in Metric Spaces

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A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density and finiteness of a geometric square function, which loosely speaking, records in an L2 gauge the extent to which μ admits approximate tangent lines, or has rapidly growing density ratios, along its support. In contrast with the classical...