• 대한수학회보
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• 제51권2호
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• pp.317-328
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• 2014

In Bae et al. [2], we have considered the uniform CLT for the martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes majorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.

• 대한수학회지
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• 제46권2호
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• pp.225-236
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• 2009

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.