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| Gaussian Measures in L^p(p \geq 2) Spaces |
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Citation： |
Zhang Yingnan.Gaussian Measures in L^p(p \geq 2) Spaces[J].Chinese Annals of Mathematics B,1982,3(2):185~188 |
| Page view： 848
Net amount： 697 |
Authors： |
Zhang Yingnan; |
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| Abstract： |
In this note we prove that if (S,F,\mu) is an \sigma-finite measure space and (x_n(t)) is sequence of L^p(S,F,\mu),p \geq 2,then the following are equivalent:
a) $[\sum {{e_n}(w){x_n}(t)} \]$ converges a.s.,where e_n(w) are independent identically distributed symmetric stable random variables of index 2,i.e.,
$E(exp(ite_n(w)))=exp(-t^2/2)$
for all t real.
b)$[\int_s {(\sum\limits_n {|{x_n}(t){|^2}{)^{p/2}}\mu (dt) < \infty } } \]$ |
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