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Metric universality for the devil's staircase of topological entropy

✍ Scribed by Jing-Xiu Shi; Ke-Fei Cao; Tian-Le Guo; Shou-Li Peng

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
335 KB
Volume
211
Category
Article
ISSN
0375-9601

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Let T d : L 2 ([0, 1] d ) Γ„ C([0, 1] d ) be the d-dimensional integration operator. We show that its Kolmogorov and entropy numbers decrease with order at least k &1 (log k) d&1Γ‚2 . From this we derive that the small ball probabilities of the Brownian sheet on [0, 1] d under the C([0, 1] d )-norm ca