Abstract
A uniform estimate of the rate of convergence in the central limit theorem (CLT) in certain Banach spaces for dependent random variables is established when the Gaussian measure of the ϵ-neighbourhood of the boundary of a set is proportional to ϵ and the third order moment is finite in the strong sense. A uniform estimate in the CLT for Banach valued dependent random variables is carried out when the B-space is well behaved for a martingale transform.
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