199 research outputs found
Attractor of Cantor Type with Positive Measure
We construct an iterated function system consisting of strictly increasing
contractions with
and such that its attractor has positive Lebesgue measure
Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion
We prove a dimension distortion estimate for mappings of sub-exponentially
integrable distortion in Euclidean spaces, which is essentially sharp in the
plane
Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings
We investigate how the integrability of the derivatives of Orlicz-Sobolev
mappings defined on open subsets of affect the sizes of the
images of sets of Hausdorff dimension less than . We measure the sizes of
the image sets in terms of generalized Hausdorff measures
Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding
We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a PoincarĂ© inequality to a Banach space with the RadonâNikodym property that guarantees differentiability at almost every point. We apply these results to obtain a non-embedding theorem for a corresponding class of mappings
The Stepanov differentiability theorem in metric measure spaces
We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As a consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequalit
- âŠ