随机级数sum from n=1 to ∞ ξ_nu_n的一些性质

Some Properties of the Random Series sum from n=1 to ∞ ξ_nu_n

对Rademacher级数sum from n=1 to ∞±un的性质进行了研究,首先将sum from n=1 to ∞±un的相关结果进行了推广,对于更为一般的随机级数sum from n=1 to ∞ξ_nu_n确定了其有限和的上确界与级数之间的具有相互限制的数量关系,然后,通过其数量关系将Rademacher级数的重要性质作了推广,通过研究发现:级数sum from n=1 to ∞ξ_nu_n具有Rademacher级数同样的确界定理.最后,直接证明了如果级数sum from n=1 to ∞ξ_nu_n收敛,它的模V属于Lp(Ω)空间.

In this paper, we study the properties of the random series ∑n=1^∞±un. First,we extend the lemma of random series to the random series ∑n=1^∞ξnun ,we found there are volume relations between its supremum of limited sum and random series. Then, we get an important result about the random series ∑n=1^∞±un. At last,a inferences could also be got.