Let K be the attractor of a linear iterated function system Sj x = Οjx + bj (j = 1, . . . , m) on the real line satisfying the open set condition (where the open set is an interval). It is well known that the packing dimension of K is equal to Ξ±, the unique positive solution y of the equation m j=1
The Packing Theorem and Packing Measure
β Scribed by Hermann Haase
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 282 KB
- Volume
- 146
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
For a VITALI class of a metric space (X, d) a packing measure is introduced following the ideas of [7]. The Packing Theorem of VITALI is a powerful mean to derive density results for measures [1, 2, 3]. Conversely, the notion of packing measure allows us to give sufficient conditions for a measure that the packing theorem of VITALI hods.
π SIMILAR VOLUMES
## Moser asked whether the collection of rectangles of dimensions .., whose total area equals 1, can be packed into the unit square without overlap, and whether the collection of squares of side lengths 1 2 , 1 3 , 1 4 , ... can be packed without overlap into a rectangle of area p 2 /6 -1. Computa