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Nonsmooth Morse–Sard theorems

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Azagra Rueda, Daniel and Ferrera Cuesta, Juan and Gómez Gil, Javier (2017) Nonsmooth Morse–Sard theorems. Nonlinear Analysis, Theory, Methods and Applicatioms, 160 . pp. 53-69. ISSN 0362546X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X17301347


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Abstract

We prove that every function f:Rn→R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n−1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof, for the proximal subdifferential ∂P, we see that for every lower semicontinuous function f:R2→R the set f({x∈R2:0∈∂Pf(x)}) is L1-null.


Item Type:Article
Uncontrolled Keywords:Morse–Sard theorem; Taylor polynomial; Subdifferential; Nonsmooth
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:43784
Deposited On:05 Jul 2017 08:19
Last Modified:05 Jul 2017 08:19

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