## Metric entropy of high dimensional distributions.(English)Zbl 1147.46018

For a collection $$T$$ of probability distributions in $$[0, 1]^d$$ having a density, the authors give estimates for the metric entropy under the $$L^2$$-norm. They obtain its exact rate for $$d=1$$ and $$d=2$$ and get bounds for $$d > 3$$. Then, they establish connections to the small deviation probability for Brownian sheets under the sup-norm.

### MSC:

 46B50 Compactness in Banach (or normed) spaces 46A50 Compactness in topological linear spaces; angelic spaces, etc. 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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### References:

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