MATHEMATICA BOHEMICA, Vol. 133, No. 4, pp. 337-340, 2008

Morse-Sard theorem for delta-convex curves

D. Pavlica

D. Pavlica, Institute of Mathematics, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: pavlica@math.cas.cz

Abstract: Let $f I\to X$ be a delta-convex mapping, where $I\subset\R$ 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.

Keywords: Morse-Sard theorem, delta-convex mapping

Classification (MSC 2000): 26A51

Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.

[Next Article] [Contents of This Number] [Contents of Mathematica Bohemica]
[Full text of the older issues of Mathematica Bohemica at DML-CZ]