Stepanoff's theorem in separable Banach spaces

Donatella Bongiorno

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 323-335
  • ISSN: 0010-2628

Abstract

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Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces.

How to cite

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Bongiorno, Donatella. "Stepanoff's theorem in separable Banach spaces." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 323-335. <http://eudml.org/doc/248226>.

@article{Bongiorno1998,
abstract = {Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces.},
author = {Bongiorno, Donatella},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Gateaux differentiable functions; Lipschitz functions at a point; Radon-Nikodym property; Gateaux differentiable; Lipschitz at a point; Radon-Nikodým property; exceptional set in the sense of Aronszajn},
language = {eng},
number = {2},
pages = {323-335},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Stepanoff's theorem in separable Banach spaces},
url = {http://eudml.org/doc/248226},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Bongiorno, Donatella
TI - Stepanoff's theorem in separable Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 323
EP - 335
AB - Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces.
LA - eng
KW - Gateaux differentiable functions; Lipschitz functions at a point; Radon-Nikodym property; Gateaux differentiable; Lipschitz at a point; Radon-Nikodým property; exceptional set in the sense of Aronszajn
UR - http://eudml.org/doc/248226
ER -

References

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  1. Aronszajn N., Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147-190. (1976) Zbl0342.46034MR0425608
  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. Zbl0302.43001MR0361770
  3. Diestel J., Uhl J.J., Jr., Vector Measures, AMS, Math. Surveys, 15, Providence, 1977. Zbl0521.46035MR0453964
  4. Federer H., Geometric Measure Theory, Springer-Verlag, Berlin, 1969. Zbl0874.49001MR0257325
  5. Mankiewicz P., On the differentiability of Lipschitz mappings in Fréchet spaces, Studia Math. 45 (1973), 15-29. (1973) Zbl0219.46006MR0331055
  6. Phelps R., Gaussian null sets and differentiability of Lipschitz map on Banach spaces, Pacific J. Math. 77 (1978), 523-531. (1978) Zbl0396.46041MR0510938
  7. Rademacher H., Über partielle und totale Differenzierbarkeit I, Math. Ann. 79 (1919), 254-269. (1919) 
  8. Stepanoff W., Über totale Differenzierbarkeit, Math. Ann. 90 (1923), 318-320. (1923) MR1512177
  9. Stepanoff W., Sur les conditions de l'existence de la differentielle totale, Rec. Math. Soc. Math. Moscou 32 (1925), 511-526. (1925) 

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