A space on which diameter-type packing measure is not Borel regular
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- by H. Joyce
- Proc. Amer. Math. Soc. 127 (1999), 985-991
- DOI: https://doi.org/10.1090/S0002-9939-99-05149-7
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Abstract:
We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.References
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- H. Haase, Non-$\sigma$-finite sets for packing measure, Mathematika 33 (1986), no. 1, 129–136. MR 859505, DOI 10.1112/S0025579300013942
- J. Bourgain, An approach to pointwise ergodic theorems, Geometric aspects of functional analysis (1986/87), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 204–223. MR 950982, DOI 10.1007/BFb0081742
- Hermann Haase, The packing theorem and packing measure, Math. Nachr. 146 (1990), 77–84. MR 1069049, DOI 10.1002/mana.19901460307
- J. D. Howroyd, On Hausdorff and packing dimension of product spaces, Math. Proc. Cambridge Philos. Soc. 119 (1996), no. 4, 715–727. MR 1362951, DOI 10.1017/S0305004100074545
- H. Joyce, Concerning the problem of subsets of finite positive packing measure. J. London Math. Soc. (2) 56 (1997), 557–566.
- H. Joyce, Packing measures, packing dimensions, and the existence of sets of positive finite measure. Thesis, University College London, 1995.
- H. Joyce and D. Preiss, On the existence of subsets of finite positive packing measure, Mathematika 42 (1995), no. 1, 15–24. MR 1346667, DOI 10.1112/S002557930001130X
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press, 1995.
- Pertti Mattila and R. Daniel Mauldin, Measure and dimension functions: measurability and densities, Math. Proc. Cambridge Philos. Soc. 121 (1997), no. 1, 81–100. MR 1418362, DOI 10.1017/S0305004196001089
- S. James Taylor and Claude Tricot, Packing measure, and its evaluation for a Brownian path, Trans. Amer. Math. Soc. 288 (1985), no. 2, 679–699. MR 776398, DOI 10.1090/S0002-9947-1985-0776398-8
- Claude Tricot Jr., Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc. 91 (1982), no. 1, 57–74. MR 633256, DOI 10.1017/S0305004100059119
Bibliographic Information
- H. Joyce
- Affiliation: Department of Mathematics, University of Jyväskylä, SF-40351 Jyväskylä, Finland
- Address at time of publication: 10 Shearwater, Orton Wistow, Peterborough, Cambs PE2 64W, England
- Email: joyce@math.jyu.fi
- Received by editor(s): December 11, 1996
- Communicated by: Christopher Croke
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 985-991
- MSC (1991): Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-99-05149-7
- MathSciNet review: 1641642