| Title:
|
Stepanoff's theorem in separable Banach spaces (English) |
| Author:
|
Bongiorno, Donatella |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
323-335 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces. (English) |
| Keyword:
|
Gateaux differentiable functions |
| Keyword:
|
Lipschitz functions at a point |
| Keyword:
|
Radon-Nikodym property |
| MSC:
|
46A65 |
| MSC:
|
46G05 |
| idZBL:
|
Zbl 0937.46038 |
| idMR:
|
MR1651959 |
| . |
| Date available:
|
2009-01-08T18:40:50Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119009 |
| . |
| Reference:
|
[1] Aronszajn N.: Differentiability of Lipschitzian mappings between Banach spaces.Studia Math. 57 (1976), 147-190. Zbl 0342.46034, MR 0425608 |
| Reference:
|
[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. Zbl 0302.43001, MR 0361770 |
| Reference:
|
[3] Diestel J., Uhl J.J., Jr.: Vector Measures.AMS, Math. Surveys, 15, Providence, 1977. Zbl 0521.46035, MR 0453964 |
| Reference:
|
[4] Federer H.: Geometric Measure Theory.Springer-Verlag, Berlin, 1969. Zbl 0874.49001, MR 0257325 |
| Reference:
|
[5] Mankiewicz P.: On the differentiability of Lipschitz mappings in Fréchet spaces.Studia Math. 45 (1973), 15-29. Zbl 0219.46006, MR 0331055 |
| Reference:
|
[6] Phelps R.: Gaussian null sets and differentiability of Lipschitz map on Banach spaces.Pacific J. Math. 77 (1978), 523-531. Zbl 0396.46041, MR 0510938 |
| Reference:
|
[7] Rademacher H.: Über partielle und totale Differenzierbarkeit I.Math. Ann. 79 (1919), 254-269. |
| Reference:
|
[8] Stepanoff W.: Über totale Differenzierbarkeit.Math. Ann. 90 (1923), 318-320. MR 1512177 |
| Reference:
|
[9] Stepanoff W.: Sur les conditions de l'existence de la differentielle totale.Rec. Math. Soc. Math. Moscou 32 (1925), 511-526. |
| . |
