| Title:
|
Morse-Sard theorem for delta-convex curves (English) |
| Author:
|
Pavlica, D. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
337-340 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $f\colon I\to X$ be a delta-convex mapping, where $I\subset \mathbb R $ is an open interval and $X$ a Banach space. Let $C_f$ be the set of critical points of $f$. We prove that $f(C_f)$ has zero $1/2$-dimensional Hausdorff measure. (English) |
| Keyword:
|
Morse-Sard theorem |
| Keyword:
|
delta-convex mapping |
| MSC:
|
26A51 |
| idZBL:
|
Zbl 1199.26037 |
| idMR:
|
MR2472482 |
| DOI:
|
10.21136/MB.2008.140622 |
| . |
| Date available:
|
2010-07-20T17:35:27Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140622 |
| . |
| Reference:
|
[1] Bourbaki, N.: Éléments de mathématique IX., Les structures fondamentales de l'analyse. Livre IV: Fonctions d'une variable réelle (théorie élémentaire).Act. Sci. et Ind. vol. 1074, Hermann, Paris (1968). |
| Reference:
|
[2] Federer, H.: Geometric Measure Theory.Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer, New York (1969). Zbl 0176.00801, MR 0257325 |
| Reference:
|
[3] Hartman, P.: On functions representable as a difference of convex functions.Pacific J. Math. 9 (1959), 707-713. Zbl 0093.06401, MR 0110773, 10.2140/pjm.1959.9.707 |
| Reference:
|
[4] Kirchheim, B.: Rectifiable metric spaces: local structure and regularity of the Hausdorff measure.Proc. Amer. Math. Soc. 121 (1994), 113-123. Zbl 0806.28004, MR 1189747, 10.1090/S0002-9939-1994-1189747-7 |
| Reference:
|
[5] Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability.Cambridge Studies in Advanced Mathematics, 44, Cambridge University Press, Cambridge (1995). Zbl 0819.28004, MR 1333890 |
| Reference:
|
[6] Pavlica, D., Zajíček, L.: Morse-Sard theorem for d. c. functions and mappings on $\mathbb R^2$.Indiana Univ. Math. J. 55 (2006), 1195-1207. MR 2244604 |
| Reference:
|
[7] Veselý, L., Zajíček, L.: Delta-convex mappings between Banach spaces and applications.Dissertationes Math. (Rozprawy Mat.) 289 (1989). MR 1016045 |
| . |
