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Keywords:
Gateaux differentiable functions; Lipschitz functions at a point; Radon-Nikodym property
Gateaux differentiable functions; Lipschitz functions at a point; Radon-Nikodym property
Summary:
Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces.
References:
[1] Aronszajn N.: Differentiability of Lipschitzian mappings between Banach spaces. Studia Math. 57 (1976), 147-190. MR 0425608 | Zbl 0342.46034
[2] Christensen J.P.R.: Measure theoretic zero sets in infinite dimensional spaces and applications to differentiability of Lipschitz mappings. 2-ieme Coll. Anal. Fonct. (1973, Bordeaux), Publ. du Dept. Math. Lyon 10-2 (1973), 29-39. MR 0361770 | Zbl 0302.43001
[3] Diestel J., Uhl J.J., Jr.: Vector Measures. AMS, Math. Surveys, 15, Providence, 1977. MR 0453964 | Zbl 0521.46035
[4] Federer H.: Geometric Measure Theory. Springer-Verlag, Berlin, 1969. MR 0257325 | Zbl 0874.49001
[5] Mankiewicz P.: On the differentiability of Lipschitz mappings in Fréchet spaces. Studia Math. 45 (1973), 15-29. MR 0331055 | Zbl 0219.46006
[6] Phelps R.: Gaussian null sets and differentiability of Lipschitz map on Banach spaces. Pacific J. Math. 77 (1978), 523-531. MR 0510938 | Zbl 0396.46041
[7] Rademacher H.: Über partielle und totale Differenzierbarkeit I. Math. Ann. 79 (1919), 254-269.
[8] Stepanoff W.: Über totale Differenzierbarkeit. Math. Ann. 90 (1923), 318-320. MR 1512177
[9] Stepanoff W.: Sur les conditions de l'existence de la differentielle totale. Rec. Math. Soc. Math. Moscou 32 (1925), 511-526.
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