THE PACKING MEASURE AND SYMMETRIC DERIVATION BASIS MEASURE-II

Meinershagen

doi:10.2307/44152294

The symmetric derivation basis measure and the packing measure

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1988-0947664-6 ◽

1988 ◽

Vol 103 (3) ◽

pp. 813-813 ◽

Cited By ~ 1

Author(s):

Sandra Meinershagen

Keyword(s):

Packing Measure

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Packing measure of the sample paths of fractional Brownian motion

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-96-01712-6 ◽

1996 ◽

Vol 348 (8) ◽

pp. 3193-3213 ◽

Cited By ~ 8

Author(s):

Yimin Xiao

Keyword(s):

Brownian Motion ◽

Fractional Brownian Motion ◽

Packing Measure ◽

Sample Paths

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Exact Hausdorff and Packing measure of certain Cantor sets, not necessarily self-similar or homogeneous

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2019.01.036 ◽

2019 ◽

Vol 474 (1) ◽

pp. 143-156 ◽

Cited By ~ 1

Author(s):

Leandro Zuberman

Keyword(s):

Cantor Sets ◽

Packing Measure ◽

Self Similar

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Dimensions of measures under orthogonal projections

Advances in Applied Probability ◽

10.2307/1428059 ◽

1996 ◽

Vol 28 (2) ◽

pp. 344-345

Author(s):

Martina Zähle

Keyword(s):

Hausdorff Dimension ◽

Packing Dimension ◽

Packing Measure ◽

Orthogonal Projections

Let dimH, E be the Hausdorff dimension and dimP, E the packing dimension of the subset E of ℝn given by the unique exponent where the corresponding Hausdorff or packing measure of E jumps from infinity to zero.

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Packing dimension and measure of homogeneous Cantor sets

Bulletin of the Australian Mathematical Society ◽

10.1017/s000497270004048x ◽

2006 ◽

Vol 74 (3) ◽

pp. 443-448 ◽

Cited By ~ 7

Author(s):

H.K. Baek

Keyword(s):

Lower Bound ◽

Explicit Formula ◽

Cantor Sets ◽

Packing Dimension ◽

Packing Measure ◽

Hausdorff Measures ◽

Packing Dimensions

For a class of homogeneous Cantor sets, we find an explicit formula for their packing dimensions. We then turn our attention to the value of packing measures. The exact value of packing measure for homogeneous Cantor sets has not yet been calculated even though that of Hausdorff measures was evaluated by Qu, Rao and Su in (2001). We give a reasonable lower bound for the packing measures of homogeneous Cantor sets. Our results indicate that duality does not hold between Hausdorff and packing measures.

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Frostman lemmas for Hausdorff measure and packing measure in a product probability space and their physical application

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2004.05.045 ◽

2005 ◽

Vol 24 (3) ◽

pp. 733-744 ◽

Cited By ~ 1

Author(s):

Chaoshou Dai ◽

Yanyan Hou

Keyword(s):

Hausdorff Measure ◽

Probability Space ◽

Physical Application ◽

Packing Measure

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The packing measure of self-affine carpets

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100072224 ◽

1994 ◽

Vol 115 (3) ◽

pp. 437-450 ◽

Cited By ~ 26

Author(s):

Yuval Peres

Keyword(s):

Packing Dimension ◽

Packing Measure ◽

Initial Pattern

AbstractWe show that the seif-affine sets considered by McMullen [15] and Bedford [2] have infinite packing measure in their packing dimension θ except when all non-empty rows of the initial pattern have the same number of rectangles. More precisely, the packing measure is infinite in the gauge tθ|logt|−1 and zero in the gauge tθ|logt|−1−δ for any δ > 0.

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