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几何rademacher级数的图的Hausdorff维数

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南京大学学报（自然科学版） 1994年第1期30卷 12-16页

作者：金宁南京大学数学系

本文证明了对任意α∈（０，１），几何Ｒａｄｅｍａｃｈｅｒ级数ｆａ＝（ｘ∈［０，１］）的图的Ｈａｕｓｄｏｒｆｆ维数为２－α．

关键词： rademacher 级数豪斯道夫维数图

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Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements

引用

Acta Mathematica Sinica,English Series 2019年第5期35卷 583-596页

作者： Robert PARKER Andrew ROSALSKY Department of Biostatistics University of Florida Department of Statistics University of Florida

For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.