The packing measure of rectifiable sets

1984 ◽  
Vol 10 (1) ◽  
pp. 58
Author(s):  
Taylor ◽  
Tricot
Keyword(s):  
Packing Measure ◽  
Rectifiable Sets

scholarly journals Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets

2008 ◽  
Vol 360 (03) ◽  
pp. 1559-1581 ◽  
Author(s):  
S. V. Borodachov ◽  
D. P. Hardin ◽  
E. B. Saff
Keyword(s):  
Riesz Energy ◽  
Rectifiable Sets

Dimensions of measures under orthogonal projections

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.

scholarly journals Packing dimension and measure of homogeneous Cantor sets

2006 ◽  
Vol 74 (3) ◽  
pp. 443-448 ◽  
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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