Download A central limit theorem for exchangeable random variables on by Bingham M.S. PDF

By Bingham M.S.

A crucial restrict theorem is given for uniformly infinitesimal triangular arrays of random variables within which the random variables in each one row are exchangeable and take values in a in the community compact moment countable abclian staff. The proscribing distribution within the theorem is Gaussian.

Show description

Read Online or Download A central limit theorem for exchangeable random variables on a locally compact abelian group PDF

Similar symmetry and group books

Analytical methods for Markov semigroups

For the 1st time in ebook shape, Analytical equipment for Markov Semigroups offers a accomplished research on Markov semigroups either in areas of bounded and non-stop features in addition to in Lp areas appropriate to the invariant degree of the semigroup. Exploring particular innovations and effects, the booklet collects and updates the literature linked to Markov semigroups.

Additional resources for A central limit theorem for exchangeable random variables on a locally compact abelian group

Example text

9) a(z;glg2)= a(z;gl)u(xgl;gz);for all gl;g2 E G , x E X . 10) does give a representation of G. Furthermore, if u is continuousfunitary and X has a Haar measure d x , then T , also becomes a continuousfunitary representation'' of G on space L 2 ( X ; Y ) , of square-integrable Y-valued functions on X (problem 9). 2. Regular representations R on G and quotients X = H\G, are induced by the trivial cocycle u, R = ind(1 I H;G). g. continuous, differentiable, L2-functions, etc. 7) to make T unitary.

In particular, unitary (or more general bounded) representations, I(T,(I5 C, yield bounded operators {T,} for all f in the group algebra with weight w, L = L'(G), indeed, I)T,(II Cllflll. 2. Regular and induced representation 33 R f [ h ]= f*h. 15) has to do with nice (smoothing/regularizing) properties of operators { T I } . To wit the “unitary/bounded group operators” {T,} could yield a better class of “algebra operators” { Tf}:compact, Hilbert-Schmidt, or trace-class. The latter often depends on the regularity properties of L = em(G);P‘(G), the “smoother11 { f ’ s } one takes the “better” { T I }results.

Regular and induced representation 33 R f [ h ]= f*h. 15) has to do with nice (smoothing/regularizing) properties of operators { T I } . To wit the “unitary/bounded group operators” {T,} could yield a better class of “algebra operators” { Tf}:compact, Hilbert-Schmidt, or trace-class. The latter often depends on the regularity properties of L = em(G);P‘(G), the “smoother11 { f ’ s } one takes the “better” { T I }results. A simple illustration is furnished by convolutions with f E Cm(G) (or Coo).

Download PDF sample

Rated 4.05 of 5 – based on 11 votes