메뉴 건너뛰기




Volumn 22, Issue 3, 2006, Pages 893-953

Coverings, derivation of measurements and dimensions;Recouvrements, derivation des mesures et dimensions

Author keywords

Covering properties; Derivation theorems; Dimensions of metric spaces

Indexed keywords


EID: 34147174310     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/rmi/478     Document Type: Article
Times cited : (10)

References (42)
  • 1
    • 85157089232 scopus 로고    scopus 로고
    • ASSOUAD, P.: Espaces métriques, plongements, facteurs. Thèse de doctorat, Publications Mathématiques d'Orsay, No. 223-7769. U.E.R. de Mathématique, Université de Paris XI, Orsay, 1977.
    • ASSOUAD, P.: Espaces métriques, plongements, facteurs. Thèse de doctorat, Publications Mathématiques d'Orsay, No. 223-7769. U.E.R. de Mathématique, Université de Paris XI, Orsay, 1977.
  • 6
    • 0001684131 scopus 로고
    • A general form of the covering principle and relative differentiation of additive functions
    • BESICOVITCH, A. S.: A general form of the covering principle and relative differentiation of additive functions. Proc. Cambridge Philos. Soc. 41 (1945), 103-110
    • (1945) Proc. Cambridge Philos. Soc , vol.41 , pp. 103-110
    • BESICOVITCH, A.S.1
  • 7
    • 85157268182 scopus 로고    scopus 로고
    • 2 -2bc cos α). In The mathematical heritage of Élie Cartan (Lyon, 1984), 9-66. Astérisque (1985), numéro hors série.
    • 2 -2bc cos α). In The mathematical heritage of Élie Cartan (Lyon, 1984), 9-66. Astérisque (1985), numéro hors série.
  • 9
    • 0037845117 scopus 로고    scopus 로고
    • A course in metric geometry
    • American Mathematical Society, Providence, RI
    • BURAGO, D., BURAGO, Y. AND IVANOV, S.: A course in metric geometry. Graduate Studies in Mathematics 33. American Mathematical Society, Providence, RI, 2001.
    • (2001) Graduate Studies in Mathematics , vol.33
    • BURAGO, D.1    BURAGO, Y.2    IVANOV, S.3
  • 10
    • 0003930292 scopus 로고
    • Comparison theorems in Riemannian geometry
    • North-Holland Publishing Co
    • CHEEGER, J. AND EBIN, D.G.: Comparison theorems in Riemannian geometry. North-Holland Mathematical Library 9. North-Holland Publishing Co., 1975.
    • (1975) North-Holland Mathematical Library , vol.9
    • CHEEGER, J.1    EBIN, D.G.2
  • 12
    • 0002171569 scopus 로고
    • Subadditivity of homogeneous norms on certain nilpotent Lie groups
    • CYGAN, J.: Subadditivity of homogeneous norms on certain nilpotent Lie groups. Proc. Amer. Math. Soc. 83 (1981), 69-70.
    • (1981) Proc. Amer. Math. Soc , vol.83 , pp. 69-70
    • CYGAN, J.1
  • 13
    • 34147129174 scopus 로고
    • A proof that Henstock's integral includes Lebesgue's
    • DAVIES, R.O. AND SCHUSS, Z.: A proof that Henstock's integral includes Lebesgue's. J. London Math. Soc. (2) 2 (1970), 561-562
    • (1970) J. London Math. Soc. (2) , vol.2 , pp. 561-562
    • DAVIES, R.O.1    SCHUSS, Z.2
  • 14
    • 85157198139 scopus 로고    scopus 로고
    • DELLACHERIE, C. AND MEYER, P.A.: Probabilités et potentiel. Chapitres I à IV. Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XV. Actualités Scientifiques et Industrielles 1372. Hermann, Paris, 1975.
    • DELLACHERIE, C. AND MEYER, P.A.: Probabilités et potentiel. Chapitres I à IV. Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XV. Actualités Scientifiques et Industrielles 1372. Hermann, Paris, 1975.
  • 17
    • 34147162299 scopus 로고
    • On a metric that characterizes dimension
    • DE GROOT, J.: On a metric that characterizes dimension. Canad. J. Math. 9 (1957), 511-514
    • (1957) Canad. J. Math , vol.9 , pp. 511-514
    • DE GROOT, J.1
  • 18
    • 85157082612 scopus 로고    scopus 로고
    • n. Lecture Notes in Mathematics 481. Springer-Verlag, Berlin-New York, 1975.
    • n. Lecture Notes in Mathematics 481. Springer-Verlag, Berlin-New York, 1975.
  • 19
    • 0003458946 scopus 로고
    • North-Holland Mathematics Studies 46. North-Holland, Amsterdam-New York
    • DE GUZMÁN, M.: Real variable methods in Fourier analysis. North-Holland Mathematics Studies 46. North-Holland, Amsterdam-New York, 1981.
    • (1981) Real variable methods in Fourier analysis
    • DE GUZMÁN, M.1
  • 21
    • 0042306345 scopus 로고
    • On the best constant for the Besicovitch covering theorem
    • FÜREDI, Z. AND LOEB, P.A.: On the best constant for the Besicovitch covering theorem. Proc. Amer. Math. Soc. 121 (1994), 1063-1073.
    • (1994) Proc. Amer. Math. Soc , vol.121 , pp. 1063-1073
    • FÜREDI, Z.1    LOEB, P.A.2
  • 22
    • 0004289448 scopus 로고
    • Academic Press
    • JECH, TH.: Set Theory. Academic Press, 1978.
    • (1978) Set Theory
    • JECH, T.1
  • 23
    • 0039469180 scopus 로고
    • Baire sets in product spaces
    • Measure theory Oberwolfach 1979, Springer, Berlin
    • KELLERER, H. G.: Baire sets in product spaces. In Measure theory (Oberwolfach 1979), 38-44. Lecture Notes in Math. 794. Springer, Berlin, 1980.
    • (1980) Lecture Notes in Math , vol.794 , pp. 38-44
    • KELLERER, H.G.1
  • 24
    • 33845212561 scopus 로고
    • Foundations for the theory of quasiconformal mappings on the Heisenberg group
    • KORÁNYI, A. AND REIM ANN, H. M.: Foundations for the theory of quasiconformal mappings on the Heisenberg group. Adv. Math. 111(1995), 1-87.
    • (1995) Adv. Math , vol.111 , pp. 1-87
    • KORÁNYI, A.1    REIM ANN, H.M.2
  • 25
    • 33644541825 scopus 로고    scopus 로고
    • Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions
    • LANG, U. AND SCHLICHENMAIER, T.: Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions. Int. Math. Res. JVbt. 2005 58, 3625-3655.
    • (2005) Int. Math. Res. JVbt , vol.58 , pp. 3625-3655
    • LANG, U.1    SCHLICHENMAIER, T.2
  • 26
    • 33748546779 scopus 로고
    • Differentiation of measures on uniform spaces
    • Measure theory Oberwolfach 1979, Springer, Berlin
    • MATTILA, P.: Differentiation of measures on uniform spaces. In Measure theory (Oberwolfach 1979), 261-283. Lecture Notes in Math. 794. Springer, Berlin, 1980.
    • (1980) Lecture Notes in Math , vol.794 , pp. 261-283
    • MATTILA, P.1
  • 27
    • 85157109755 scopus 로고    scopus 로고
    • MEYER, P.A.: Probabilités et potentiel. Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XIV. Actualités Scientifiques et Industrielles 1318. Hermann, Paris, 1966.
    • MEYER, P.A.: Probabilités et potentiel. Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XIV. Actualités Scientifiques et Industrielles 1318. Hermann, Paris, 1966.
  • 28
    • 85157086985 scopus 로고    scopus 로고
    • MORSE, A. P.: Perfect blankets. Trans. Amer. Math. Soc. 61 (1947), 418-442.
    • MORSE, A. P.: Perfect blankets. Trans. Amer. Math. Soc. 61 (1947), 418-442.
  • 29
    • 0004029364 scopus 로고
    • Unified integration
    • Academic Press, New York
    • MCSHANE, E. J.: Unified integration. Pure and Applied Mathematics 107. Academic Press, New York, 1983.
    • (1983) Pure and Applied Mathematics , vol.107
    • MCSHANE, E.J.1
  • 30
    • 34147186292 scopus 로고
    • On a special metric and dimension
    • NAGATA, J. I.: On a special metric and dimension. Fund. Math. 55 (1964), 181-194.
    • (1964) Fund. Math , vol.55 , pp. 181-194
    • NAGATA, J.I.1
  • 31
    • 85157288406 scopus 로고    scopus 로고
    • OSTRAND, P.A.: A conjecture of J. Nagata on dimension and metrization. Bull. Amer. Math. Soc. 71 (1965), 623-625.
    • OSTRAND, P.A.: A conjecture of J. Nagata on dimension and metrization. Bull. Amer. Math. Soc. 71 (1965), 623-625.
  • 32
    • 0003660341 scopus 로고
    • Measure and Category. A survey of the analogies between topological and measure spaces
    • Springer-Verlag, New York-Berlin
    • OXTOBY, J. C.: Measure and Category. A survey of the analogies between topological and measure spaces. Graduate Texts in Mathematics 2. Springer-Verlag, New York-Berlin, 1971.
    • (1971) Graduate Texts in Mathematics , vol.2
    • OXTOBY, J.C.1
  • 33
    • 11144301661 scopus 로고
    • Dimension of metrics and differentiation of measures
    • General topology and its relations to modern analysis and algebra, V Prague, 1981, Heldermann, Berlin
    • PREISS, D.: Dimension of metrics and differentiation of measures. In General topology and its relations to modern analysis and algebra, V (Prague, 1981), 565-568. Sigma Ser. Pure Math. 3. Heldermann, Berlin, 1983.
    • (1983) Sigma Ser. Pure Math , vol.3 , pp. 565-568
    • PREISS, D.1
  • 34
    • 85157285054 scopus 로고
    • Another proof that Riemann-complete integral includes the Lebesgue integral
    • PU, H.W.: Another proof that Riemann-complete integral includes the Lebesgue integral. Bull. Soc. Roy. Sci. Liège 41 (1972), 250-251.
    • (1972) Bull. Soc. Roy. Sci. Liège , vol.41 , pp. 250-251
    • PU, H.W.1
  • 35
    • 0012694834 scopus 로고
    • Die innere Geometrie der metrischen Raüme
    • Springer-Verlag, Berlin-Göttingen-Heidelberg
    • RINOW, W.: Die innere Geometrie der metrischen Raüme. Die Grundlehren der mathematischen Wissenschaften 105. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961.
    • (1961) Die Grundlehren der mathematischen Wissenschaften , vol.105
    • RINOW, W.1
  • 36
    • 0003799686 scopus 로고
    • Singular integrals and differentiability properties of functions
    • Princeton University Press, Princeton, N.J
    • STEIN. E. M.: Singular integrals and differentiability properties of functions. Princeton Mathematical Series 30. Princeton University Press, Princeton, N.J. 1970
    • (1970) Princeton Mathematical Series , vol.30
    • STEIN, E.M.1
  • 37
    • 34147125427 scopus 로고
    • Sphere packings give an explicit bound for the Besicovitch covering theorem
    • SULLIVAN, J. M.: Sphere packings give an explicit bound for the Besicovitch covering theorem. J. Geom. Anal. 4 (1994), 219-231.
    • (1994) J. Geom. Anal , vol.4 , pp. 219-231
    • SULLIVAN, J.M.1
  • 38
    • 0000444043 scopus 로고
    • Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces
    • SAWYER, E. AND WHEEDEN, R. L.: Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces. Amer. J. Math. 114 (1992), 813-874.
    • (1992) Amer. J. Math , vol.114 , pp. 813-874
    • SAWYER, E.1    WHEEDEN, R.L.2
  • 39
    • 0000505636 scopus 로고
    • Zur Masstheorie in der allgemeinen Mengenlehre
    • ULAM, S.: Zur Masstheorie in der allgemeinen Mengenlehre. Fund. Math. 16 (1930), 140-150.
    • (1930) Fund. Math , vol.16 , pp. 140-150
    • ULAM, S.1
  • 40
    • 50449110944 scopus 로고    scopus 로고
    • Weak convergence and empirical processes. With applications to statistics
    • Springer-Verlag, New York
    • VAN DER VAART, A. W. AND WELLNER, J. A.: Weak convergence and empirical processes. With applications to statistics. Springer Series in Statistics. Springer-Verlag, New York, 1996.
    • (1996) Springer Series in Statistics
    • VAN DER VAART, A.W.1    WELLNER, J.A.2
  • 41
    • 84971184270 scopus 로고
    • On measure derivation in metric spaces
    • ZANZOTTO, P. A.: On measure derivation in metric spaces. Mathematika 36 (1989), 349-358.
    • (1989) Mathematika , vol.36 , pp. 349-358
    • ZANZOTTO, P.A.1
  • 42
    • 0004095766 scopus 로고
    • Weakly differentiate functions. Sobolev spaces and functions of bounded variation
    • SpringerVerlag, New York
    • ZIEMER, W. P.: Weakly differentiate functions. Sobolev spaces and functions of bounded variation. Graduate Texts in Mathematics 120. SpringerVerlag, New York, 1989.
    • (1989) Graduate Texts in Mathematics , vol.120
    • ZIEMER, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.