Typical dimension of the graph of certain functions
✍ Scribed by Jörg Schmeling; Reinhard Winkler
- Publisher
- Springer Vienna
- Year
- 1995
- Tongue
- English
- Weight
- 581 KB
- Volume
- 119
- Category
- Article
- ISSN
- 0026-9255
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📜 SIMILAR VOLUMES
Previously, L. Olsen had studied the typical behavior (in the sense of Baire's category) of the upper and lower L q -dimensions of a single measure. In this paper, we will focus on the typical behavior of the upper and lower mixed L q -dimensions of finitely many measures.
A graph is a pair (V, I), V being the vertices and I being the relation of adjacency on V. Given a grqh G, then a collection of functions (fi}~ ,, each fi mapping each vertex of V into an arc on a fixed circle, is said to define an m-arc intersection model for G if for all x, y E V, xly e=, (Vi~ml(f
We show that the order dimension of the complete graph on n vertices is the smallest integer t for which there are n antichains in the subset lattice of It -1] that do not contain [t -1] or two sets whose union is [t-1].