Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We find a condition for a Borel mapping $f:ℝ^m → ℝ^n$ which implies that the Hausdorff dimension of $f^{-1}(y)$ is less than or equal to m-n for almost all $y ∈ ℝ^n$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
217-221
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-09-16
Twórcy
autor
- Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
- [1] B. Bojarski and P. Hajłasz, in preparation.
- [2] Y. Burago and V. Zalgaller, Geometric Inequalities, Grundlehren Math. Wiss. 285, Springer, 1988.
- [3] S. Eilenberg, On $ϕ$-measures, Ann. Soc. Polon. Math. 17 (1938), 252-253.
- [4] S. Eilenberg and O. Harold, Continua of finite linear measure I, Amer. J. Math. 65 (1943), 137-146.
- [5] H. Federer, Geometric Measure Theory, Springer, 1969.
- [6] P. Hajłasz, A note on weak approximation of minors, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.
- [7] P. Hajłasz, Sobolev mappings, co-area formula and related topics, preprint.
- [8] T. Jech, Set Theory, Acad. Press, 1978.
- [9] K. Kuratowski, Topology, Vol. 1, Acad. Press, 1966.
- [10] N. Lusin, Sur les ensembles analytiques, Fund. Math. 10 (1927), 1-95.
- [11] N. Lusin et W. Sierpiński, Sur quelques propriétés des ensembles \rm (A), Bull. Acad. Cracovie 4-5A (1918), 35-48.
- [12] P. Mattila, Hausdorff dimension, orthogonal projections and intersections with planes, Ann. Acad. Sci. Fenn. Ser. A I Math. 1 (1975), 227-244.
- [13] J. Milnor, Topology from the Differentiable Viewpoint, The Univ. Press of Virginia, 1965.
- [14] A. Sard, The measure of the critical values of differentiable maps, Bull. Amer. Math. Soc. 48 (1942), 883-890.
- [15] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, N.J., 1964.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv67i2p217bwm