On Stepanov type differentiability theorems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10318980" target="_blank" >RIV/00216208:11320/15:10318980 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10474-014-0465-6" target="_blank" >http://dx.doi.org/10.1007/s10474-014-0465-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10474-014-0465-6" target="_blank" >10.1007/s10474-014-0465-6</a>

Result language
angličtina
Original language name
On Stepanov type differentiability theorems
Original language description
The main result shows that the Rademacher theorem proved by J. Lindenstrauss and D. Preiss in 2003 (which says that, for some pairs X, Y of Banach spaces, each Lipschitz f: X -> Y is Gamma-a.e. Fréchet differentiable) generalizes to the corresponding Stepanov theorem (which says that, for such X and Y, an arbitrary f: X -> Y is Fréchet differentiable at Gamma-almost all points at which f is Lipschitz). We also present an abstract approach which shows an easy way how (in some cases) a theorem of Stepanovtype (for vector functions) can be inferred from the corresponding theorem of Radamacher type. Finally we present Stepanov type differentiability theorems with the assumption of pointwise directional Lipschitzness.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F12%2F0436" target="_blank" >GAP201/12/0436: Theory of Real Functions and Descriptive Set Theory III</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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