A central limit theorem for convex sets
โ Scribed by B. Klartag
- Publisher
- Springer-Verlag
- Year
- 2007
- Tongue
- English
- Weight
- 481 KB
- Volume
- 168
- Category
- Article
- ISSN
- 0020-9910
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๐ SIMILAR VOLUMES
A complete characterisation is given of the class of all doublets which determine the rate of convergence in the central limit theorem. This enables a number of important properties of convergence determining sets to be deduced. In particular, it is shown that no singleton can be convergence determi
A set S in 1 :" is said to he X,-convex if and only if S does not contain a visually independent subset having cardinality h', . It is natural tts ask when an h',-convex set may be expressed as a countable unI.,n of convex sets. Here i! is proved that if S is a closed h',-convex set in the plane and
We give central limit theorems for generalized set-valued random variables whose level sets are compact both in R d or in a Banach space under milder conditions than those obtained recently by the latter two authors.