University of Birmingham > Talks@bham > Analysis Seminar > Differentiability of typical Lipschitz functions

## Differentiability of typical Lipschitz functionsAdd to your list(s) Download to your calendar using vCal - Olga Maleva (University of Birmingham)
- Monday 29 November 2021, 15:00-16:00
- Lecture Theatre C, Watson Building.
If you have a question about this talk, please contact Jon Bennett. This talk is devoted to differentiability properties of Lipschitz functions. The classical Rademacher Theorem guarantees that every Lipschitz function between finite-dimensional spaces is differentiable almost everywhere. This means that for every set T of positive Lebesgue measure and for every Lipschitz function f defined on the whole space the set of points from T where f is differentiable is non-empty and is ‘much larger’ than the set of points where it is not differentiable. A major direction in geometric measure theory research of the last two decades has been to explore to what extent this is true for Lebesgue null sets. Even for real-valued Lipschitz functions, there are null subsets S of R Some sets T which are not UDS still have the property that a Surprisingly though, no matter how good the set T is, it turns out that a typical 1-Lipschitz function is non-differentiable at a typical point of T. As above, ‘typical’ is used in the sense of Baire category. The results in the talk are based on two joint papers with Michael Dymond. This talk is part of the Analysis Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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