scholarly journals Dimension of the Boundary in Different Metrics

2013 ◽  
Vol 112 (2) ◽  
pp. 275
Author(s):  
Riku Klén ◽  
Ville Suomala
Keyword(s):  
Packing Dimensions ◽  
Euclidean Domains

We consider metrics on Euclidean domains $\Omega\subset\mathbf{R}^n$ that are induced by continuous densities $\rho\colon\Omega\rightarrow(0,\infty)$ and study the Hausdorff and packing dimensions of the boundary of $\Omega$ with respect to these metrics.

U.F.D., P.I.D. and Euclidean Domains

2017 ◽  
pp. 393-416
Author(s):  
Claudia Menini ◽  
Freddy Van Oystaeyen
Keyword(s):  
Euclidean Domains

scholarly journals Standard bases over Euclidean domains

2021 ◽  
Vol 102 ◽  
pp. 21-36
Author(s):  
Christian Eder ◽  
Gerhard Pfister ◽  
Adrian Popescu
Keyword(s):  
Standard Bases ◽  
Euclidean Domains

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.

Projection theorems for box and packing dimensions

1996 ◽  
Vol 119 (2) ◽  
pp. 287-295 ◽  
Author(s):  
K. J. Falconer ◽  
J. D. Howroyd
Keyword(s):  
Orthogonal Projection ◽  
Packing Dimension ◽  
Analytic Subset ◽  
Box Counting ◽  
Packing Dimensions ◽  
Image Position ◽  
Almost All ◽  
Projection Theorems

AbstractWe show that if E is an analytic subset of ℝn thenfor almost all m–dimensional subspaces V of ℝn, where projvE is the orthogonal projection of E onto V and dimp denotes packing dimension. The same inequality holds for lower and upper box counting dimensions, and these inequalities are the best possible ones.

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