ED431 发表于 2025-3-21 19:56:11

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他去就结束 发表于 2025-3-22 00:11:47

The Ball Sigma-Field and Measurability of Supremae two .-fields are equal for separable spaces (Problems 1.7.3 and 1.7.4). For some nonseparable spaces, it is even fairly common that maps are ball measurable even though they are not Borel measurable. Thus one may wonder about the possibility of a weak convergence theory for ball measurable maps. I

cravat 发表于 2025-3-22 04:22:02

Convergence: Almost Surely and in Probabilityhastic convergence, stronger than weak convergence. In this section we consider their nonmeasurable extensions together with the concept of almost uniform convergence, which is equivalent to outer almost sure convergence for sequences, but stronger and more useful for general nets.

preservative 发表于 2025-3-22 05:37:57

Convergence: Almost Surely and in Probabilityhastic convergence, stronger than weak convergence. In this section we consider their nonmeasurable extensions together with the concept of almost uniform convergence, which is equivalent to outer almost sure convergence for sequences, but stronger and more useful for general nets.

Pantry 发表于 2025-3-22 09:54:08

Uniformity and Metrizationgence over certain subsets. These subsets can be fairly big: equicontinuity and boundedness suffice. On the other hand, there also exist small (countable) subsets such that pointwise convergence on such a subset is automatically uniform, and equivalent to pointwise convergence on the whole of ..(D),

Ataxia 发表于 2025-3-22 14:13:00

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handle 发表于 2025-3-22 20:54:55

Uniformity and Metrizationgence over certain subsets. These subsets can be fairly big: equicontinuity and boundedness suffice. On the other hand, there also exist small (countable) subsets such that pointwise convergence on such a subset is automatically uniform, and equivalent to pointwise convergence on the whole of ..(D),

革新 发表于 2025-3-23 01:02:41

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过滤 发表于 2025-3-23 04:45:54

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BET 发表于 2025-3-23 07:07:22

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查看完整版本: Titlebook: Weak Convergence and Empirical Processes; With Applications to Aad W. Vaart,Jon A. Wellner Book 19961st edition Springer Science+Business M