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For every doubling gauge g, we prove that there is a Cantor set of positive finite Hg-measure, Pg-measure, and Pg 0 -premeasure. Also, we show that every compact metric space of infinite Pg 0 -premeasure has a compact countable subset of infinite Pg 0 -premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with F = E∪F, and a doubling gauge g such that E ∪ F has different positive finite Pg-measure and Pg 0 -premeasure.
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참고문헌 (17)
참고문헌 신청
A. Dvoretzky / 1948 / A note on Hausdorff dimension functions / Math. Pro. Camb. Phil. Soc 44 : 13 ~ 16
C. Rogers / 1998 / Hausdorff Measures / Cambridge University Press
C. Tricot / 1982 / Two definitions of fractional dimension / Math. Pro. Cambridge Philos. Soc 91 (1) : 57 ~ 74
D. J. Feng / 1995 / Dimensions and gauges for symmetric cantor sets / Approx. Theory Appl 11 (4) : 108 ~ 110
D. J. Feng / 1997 / Some dimensional results for homogeneous Moran sets / Sci. China Ser. A 40 (5) : 475 ~ 482
C. Rogers / 1998 / Hausdorff Measures / Cambridge University Press
C. Tricot / 1982 / Two definitions of fractional dimension / Math. Pro. Cambridge Philos. Soc 91 (1) : 57 ~ 74
D. J. Feng / 1995 / Dimensions and gauges for symmetric cantor sets / Approx. Theory Appl 11 (4) : 108 ~ 110
D. J. Feng / 1997 / Some dimensional results for homogeneous Moran sets / Sci. China Ser. A 40 (5) : 475 ~ 482
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