Previous |  Up |  Next

Article

Title: Obecná teorie derivování funkcí a měr na katedře matematické analýzy MFF UK (Czech)
Title: General theory of differentiation of functions and measures studied at the Charles University (English)
Author: Zajíček, Luděk
Language: Czech
Journal: Pokroky matematiky, fyziky a astronomie
ISSN: 0032-2423
Volume: 45
Issue: 3
Year: 2000
Pages: 188-207
.
Category: math
.
MSC: 01A73
MSC: 26-02
MSC: 26-03
MSC: 26A24
MSC: 26A27
MSC: 26A30
MSC: 26B05
idZBL: Zbl 1055.01022
.
Date available: 2010-12-11T18:01:36Z
Last updated: 2012-08-25
Stable URL: http://hdl.handle.net/10338.dmlcz/141037
.
Reference: [ABBM] Agronsky, S. J., Biskner, R., Bruckner, A. M., Mařík, J.: Representations of functions by derivatives.Trans. Amer. Math. Soc. 263 (1981), 493–500. MR 0594421
Reference: [AP] Aversa, V., Preiss, D.: Hearts density theorems.Real Anal. Exchange 13 (1987/88), 28–32.
Reference: [ALP] Aversa, V., Laczkovich, M., Preiss, D.: Extension of differentiable functions.Comment. Math. Univ. Carolinae 26 (1986), 597–609. MR 0817830
Reference: [BBM] Blažek, J., Borák, E., Malý, J.: On Köpcke and Pompeiu functions.Časopis Pěst. Mat. 103 (1978), 53–61.
Reference: [BCEH] Belna, C. L., Cargo, G. T., Evans, M. J., Humke, P. D.: Analogues of the Denjoy-Young-Saks theorem.Trans. Amer. Math. Soc. 271 (1982), 253–260. Zbl 0486.26003, MR 0648091
Reference: [Be] Berman, S. M.: Gaussian process with stationary increments: local times and sample function properties.Ann. Math. Statist. 41 (1970), 1260–1272. MR 0272035
Reference: [BEH] Belna, C. L., Evans, M. J., Humke, P. D.: Symmetric and ordinary differentiation.Proc. Amer. Math. Soc. 72 (1978), 261–267. Zbl 0411.26004, MR 0507319
Reference: [BL] Benyamini, Y., Lindenstrauss, J.: Geometric Nonlinear Functional Analysis.Vol. 1: Colloq. publications (American Mathematical Society); v. 48: Providence, Rhode Island 2000. Zbl 0946.46002, MR 1727673
Reference: [BP] Borwein, J. M., Preiss, D.: A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions.Trans. Amer. Math. Soc. 303 (1987), 517–527. Zbl 0632.49008, MR 0902782
Reference: [Br] Bruckner, A. M.: Differentiation of Real Functions.CRM Monographs Series, vol. 5, Providence 1994. Zbl 0796.26004, MR 1274044
Reference: [Bu] Buczolich, Z.: The $n$-dimensional gradient has the 1-dimensional DenjoyC̄larkson property.Real Anal. Exchange 18 (1992–93), 221–224. MR 1205514
Reference: [Fa] Fabian, M.: Gâteaux differentiability of convex functions and topology — weak Asplund spaces.John Wiley and Sons, Interscience 1997. Zbl 0883.46011, MR 1461271
Reference: [Fe] Federer, H.: Geometric Measure Theory.Springer-Verlag, Berlin–New York 1969. Zbl 0176.00801, MR 0257325
Reference: [FM] Fonseca, I., Malý, J.: Relaxation of multiple integrals below the growth exponent.Anal. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), 309–338. MR 1450951
Reference: [Fo] Foran, J.: The symmetric and ordinary derivative.Real Anal. Exchange 2 (1977), 105–108. Zbl 0376.26005
Reference: [Fr] Freiling, Ch.: On the problem of characterizing derivatives.Real Anal. Exchange 23 (1997/98), 805–812. Zbl 0943.26014, MR 1639989
Reference: [Gu] Guzmán, M. de: Differentiation of integrals in ${\mathbb {R}}^n$.Lecture Notes in Math. 481, Springer-Verlag, Berlin, New York 1975. MR 0457661
Reference: [HMWZ] Holický, P., Malý, J., Weil, C. E., Zajíček, L.: A note on the gradient problem.Real Anal. Exchange 22 (1996/97), 225–235. MR 1433610
Reference: [HŠZ] Holický, P., Šmídek, M., Zajíček, L.: Convex functions with nonmeasurable set of Gâteaux differentiability points.Comment. Math. Univ. Carolinae 39 (1998), 469–482. MR 1666778
Reference: [Hu] Hunt, B. R.: The prevalence of continuous nowhere differentiable functions.Proc. Amer. Math. Soc. 122 (1994), 711–717. Zbl 0861.26003, MR 1260170
Reference: [Chl] Chlebík, M.: Geometrická teória miery.Diplomová práce, MFF UK 1984.
Reference: [Cho] Choquet, Ch.: Application des propriétés descriptives de la fonction contingent a la théorie des fonctions de variable réelle et a la géometrie différentielle des variétés cartésiennes (These).J. Math. Pures Appl. 26 (1947), 115–256.
Reference: [Ke] Kelar, V.: On the first and the fifth class of Zahorski.Real Anal. Exchange 9 (1983/84), 233–250. MR 0742787
Reference: [Ki1] Kirchheim, B.: Uniformly distributed measures, tangent measures and analytic varieties.Collection: Proceedings of the Conference: Topology and Measure V (Binz, 1987), 54–60. MR 1029559
Reference: [Ki2] 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
Reference: [KKM] Kauhanen, J., Koskela, P., Malý, J.: On functions with derivatives in a Lorentz space.Manuscripta Math. 100 (1999), 87–101. MR 1714456
Reference: [KM] Kilpeläinen, T., Malý, J.: Sobolev inequalities on sets with irregular boundaries.Z. Anal. Angew. 19 (2000), 369–380. MR 1768998
Reference: [Ko] Kolář, J.: Nowhere approximately differentiable and nowhere Hölder continuous functions — Porous sets and Haar null sets.Proc. Amer. Math. Soc. (v tisku).
Reference: [KP] Kowalski, O., Preiss, D.: Besicovitch-type properties of measures and submanifolds.J. Reine Angew. Math. 379 (1987), 115–151. Zbl 0618.53006, MR 0903637
Reference: [LMZ] Lukeš, J., Malý, J., Zajíček, L.: Fine Topology Methods in Real Analysis and Potential Theory.Lecture Notes in Math. 1189, Springer–Verlag, Berlin, New York 1986.
Reference: [Mal1] Malý, J.: The Darboux property for gradients.Real Anal. Exchange 22 (1996/97), 167–173. MR 1433604
Reference: [Mal2] Malý, J.: Where the continuous functions without unilateral derivatives are typical.Trans. Amer. Math. Soc. 283 (1984), 169–175. MR 0735414
Reference: [Mal3] Malý, J.: Hölder type quasicontinuity.Potential Anal. 2 (1993), 249–254. MR 1245242
Reference: [Mal4] Malý, J.: Absolutely continuous functions of several variables.J. Math. Anal. Appl. 231 (1999), 492–508. MR 1669167
Reference: [Mal5] Malý, J.: A simple proof of the Stepanov theorem on differentiability almost everywhere.Expo. Math. 17 (1999), 59–61. MR 1687460
Reference: [Mal6] Malý, J.: Sufficient conditions for change of variables in integral.Preprint MFF UK, KMA-2000-19, Proceedings “Analysis and Geometry”, Novosibirsk 1999 (v tisku).
Reference: [Max] Maximoff, I.: Sur la transformation continue de quelques fonctions en dérivées exactes.Bull. Soc. Phys. Math. Kazan (3) 12 (1940), 57–81. Zbl 0063.03850, MR 0015456
Reference: [MM] Malý, J., Martio, O.: Lusin’s condition (N) and mappings of the class $W^{1,n}$.J. Reine Angew. Math. 458 (1995), 19–36. MR 1310951
Reference: [MP] Malý, J., Pick, L.: An elementary proof of sharp Sobolev embeddings.Preprint MFF UK, MATH-KMA-2000/33, Proc. Amer. Math. Soc. (v tisku). MR 1862137
Reference: [MPZ] Malý, J., Preiss, D., Zajíček, L.: An unusual monotonicity theorem with applications.Proc. Amer. Math. Soc. 102 (1988), 925-932. MR 0934869
Reference: [MPT] Mejlbro, L., Preiss, D., Tišer, J.: Differentiation and determination of measures.(připravovaná kniha).
Reference: [MZ] Malý, J., Zajíček, L.: Approximate differentiation: Jarník points.Fund. Math. 140 (1991), 87–97. MR 1139090
Reference: [Ph] Phelps, R. R.: Convex functions, monotone operators and differentiability.Lecture Notes in Math. 1364, Springer-Verlag, Berlin 1993. MR 1238715
Reference: [Pr1] Preiss, D.: Gaussian measures and covering theorems.Comment. Math. Univ. Carolinae 20 (1979), 95–99. Zbl 0386.28015, MR 0526149
Reference: [Pr2] Preiss, D.: Maximoff’s theorem.Real Anal. Exchange 5 (1979–80), 92–104. MR 0557966
Reference: [Pr3] Preiss, D.: Gaussian measures and the density theorem.Comment. Math. Univ. Carolinae 22 (1981), 181–193. Zbl 0459.28015, MR 0609946
Reference: [Pr4] Preiss, D.: Level sets of derivatives.Trans. Amer. Math. Soc. 272 (1982), 161–184. Zbl 0508.26001, MR 0656484
Reference: [Pr5] Preiss, D.: Algebra generated by derivatives.Real Anal. Exchange 8 (1982–83), 208–216. MR 0694508
Reference: [Pr6] Preiss, D.: Dimension of metrics and differentiation of measures.In collection: General topology and its relations to modern analysis and algebra, V (Prague, 1981). Sigma Ser. Pure Math. 3, Heldermann, Berlin 1983, 565–568. MR 0698459
Reference: [Pr7] Preiss, D.: Geometry of measures in ${\mathbb {R}}^n$: distribution, rectifiability, and densities.Ann. Math. 125 (1987), 537–643. MR 0890162
Reference: [Pr8] Preiss, D.: Differentiability of Lipschitz functions in Banach spaces.J. Funct. Anal. 91 (1990), 312–345. MR 1058975
Reference: [Pr9] Preiss, D.: The work of Professor Jarník in Real Analysis.In collection: Life and work of Vojtěch Jarník, B. Novák ed., Prometheus 1999, 55–65.
Reference: [PPN] Preiss, D., Phelps, R. R., Namioka, I.: Smooth Banach spaces, weak Asplund spaces and monotone or usco mappings.Israel J. Math. 72 (1990), 257–279. Zbl 0757.46028, MR 1120220
Reference: [PŠ] Preiss, D., Šverák, V.: Derivatives of type $1$.Real Anal. Exchange (1986/87), 354–360. MR 0873904
Reference: [PZ1] Preiss, D., Zajíček, L.: On the symmetry of approximate Dini derivates of arbitrary functions.Comment. Math. Univ. Carolinae 23 (1982), 691–697. MR 0687564
Reference: [PZ2] Preiss, D., Zajíček, L.: Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions.Rend. Circ. Mat. Palermo (2) Suppl. no. 3 (1984), 219–223.
Reference: [PZ3] Preiss, D., Zajíček, L.: On Dini and approximate Dini derivates of typical continuous functions.Preprint MFF UK, KMA-1999-13, Real Anal. Exchange (v tisku). MR 1825518
Reference: [PZ4] Preiss, D., Zajíček, L.: Directional derivatives of Lipschitz functions.Preprint MFF UK, KMA-2000-28. MR 1853802
Reference: [S1] Saks, S.: On the functions of Besicovitch in the space of continuous functions.Fund. Math. 19 (1932), 211–219. Zbl 0005.39105
Reference: [S2] Saks, S.: Theory of the Integral.Monogr. Matematyczne 7, New York 1937. Zbl 0017.30004
Reference: [Th1] Thomson, B. S.: Real Functions.Lecture Notes in Math. 1170, Springer-Verlag, Berlin 1985. MR 0818744
Reference: [Th2] Thomson, B. S.: Symmetric properties of real functions.M. Dekker, New York 1994. Zbl 0809.26001, MR 1289417
Reference: [Ti] Tišer, J.: Differentiation theorem for Gaussian measures on Hilbert space.Trans. Amer. Math. Soc. 308 (1988), 655–666. MR 0951621
Reference: [U1] Uher, J.: Symmetrically differentiable functions are differentiable almost everywhere.Real Anal. Exchange 8 (1982/83), 253–261. MR 0694513
Reference: [U2] Uher, J.: Symmetric semicontinuity implies continuity.Trans. Amer. Math. Soc. 293 (1986), 421–429. Zbl 0601.26003, MR 0814930
Reference: [Zh] Zahorski, Z.: Sur la première dérivée.Trans. Amer. Math. Soc. 69 (1950), 1–54. Zbl 0038.20602, MR 0037338
Reference: [Zj1] Zajíček, L.: On the differentiation of convex functions in finite and infinite dimensional spaces.Czechoslovak Math. J. 29 (1979), 340–348. MR 0536060
Reference: [Zj2] Zajíček, L.: On the symmetry of Dini derivates of arbitrary functions.Comment. Math. Univ. Carolinae 22 (1981), 195–209. MR 0609947
Reference: [Zj3] Zajíček, L.: Porosity and $\sigma $-porosity.Real Anal. Exchange 13 (1987/88), 314–350. MR 0943561
Reference: [Zj4] Zajíček, L.: The differentiability structure of typical functions in $C[0,1]$.Real Anal. Exchange 13 (1987/88), 119, 113–116, 93.
Reference: [Zj5] Zajíček, L.: Unpublished results of K. Pekár and H. Zlonická on preponderant derivatives and $M_4$ sets.Real Anal. Exchange 15 (1989/90), 413–418. MR 1042561
Reference: [Zj6] Zajíček, L.: On preponderant differentiability of typical continuous functions.Proc. Amer. Math. Soc. 124 (1996), 789–798. MR 1291796
Reference: [Zj7] Zajíček, L.: Ordinary derivative via symmetric derivative and Lipschitz condition via symmetric Lipchitz condition.Real Anal. Exchange 23 (1997/98), 653–669. MR 1640004
Reference: [Zj8] Zajíček, L.: On results of Jan Mařík in the theory of derivatives.Math. Bohem. 121 (1996), 385–395. MR 1428141
Reference: [Zj9] Zajíček, L.: Differentiability properties of typical continuous functions.Real Anal. Exchange 25 (1999/2000), 149–157.
Reference: [Zm] Ziemer, W.: Weakly differentiable functions.Graduate Texts in Mathematics 120, Springer-Verlag, New York 1989. Zbl 0692.46022, MR 1014685
Reference: [ZP] Zelený, M., Pelant, J.: The structure of the $\sigma $-ideal of $\sigma $-porous sets.Preprint MFF UK, KMA-1999-01. MR 2076859
.

Files

Files Size Format View
PokrokyMFA_45-2000-3_2.pdf 358.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo