RT Journal Article
T1 Subdifferentiable functions satisfy Lusin properties of class C^{1} or C^{2}
A1 Azagra Rueda, Daniel
A1 Ferrera Cuesta, Juan
A1 García Bravo, Miguel
A1 Gómez Gil, Javier
AB Let f : Rn →Rbeafunction.Assumethat for a measurable set Ω and almost every x ∈ Ω there exists a vector ξx ∈ Rn such thatLim inf h→0    f (x +h)− f(x)−⟨ξx,h⟩ / |h|2  >−∞.Then we show that f satisfies a Lusin-type property of order 2 in Ω, that is to say, for every ε > 0 there exists a function g ∈ C2(Rn) such that Ln({x ∈ Ω : f(x) ̸= g(x)}) ≤ ε. In particular every function which has a nonempty proximal subdifferential almost everywhere also has the Lusin property of class C2. We also obtain a similar result (replacing C2 with C1) for the Fréchet subdifferential. Finally we provide some examples showing that these kinds of results are no longer true for Taylor subexpansions of higher order.
PB Elsevier
YR 2018
FD 2018
LK https://hdl.handle.net/20.500.14352/117923
UL https://hdl.handle.net/20.500.14352/117923
LA eng
NO Ministerio de Economía, Industria y Competitividad
DS Docta Complutense
RD 6 abr 2025