On Whitney-type Characterization of Approximate Differentiability on Metric Measure Spaces
Printed: Aug 2014
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting.
As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, $BV$ and maximal functions.
approximate differentiability, metric space, strong measurable differentiable structure, Whitney theorem
26B05 - Continuity and differentiation questions
28A15 - Abstract differentiation theory, differentiation of set functions [See also 26A24]
28A75 - Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems