Abstract
In this paper, we introduce the concept of uniform differentiability which seems to be, in the class of differentiable functions, a counter part of the well-known principle of uniform integrability in measure theory. Some compactness results are obtained as well as statements concerning the passage to the limit with differential operator.
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References
Boboc, N.: Analiză Matematică I. II. Editura Univ, Bucureşti (1999)
Bourbaki, N.: Fonction d’une variable réelle (Théorie élémentaire). Hermann, Calw (1961)
Chilov, G.: Analyse mathematique. Fonctions d’une variable I. Mir (1973)
Dieudonné, G.: Éléments d’analyse I. Gaulier-Villars (1969)
Meyer, P.A.: Probability and Potentials. Blaisdell Publishing Company, Waltham (1966)
Nicolescu, M.: Analiză Matematică I, II. Ed. Tehnică, 1957 (1958)
Rudin, W.: Principles of Mathematical Analysis. McGraw-Hill, New York (1964)
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Bucur, I. Compactness Results in the Class of Differentiable Functions. Mediterr. J. Math. 19, 169 (2022). https://doi.org/10.1007/s00009-022-02081-8
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DOI: https://doi.org/10.1007/s00009-022-02081-8
Keywords
- Uniform differentiability
- completeness and compactness with respect to pointwise topology
- thickness-regularity of a set