$L_\infty$ 中 Rademacher 混沌的随机无条件收敛性及加权图与超图偏差的锐估计
Random unconditional convergence of Rademacher chaos in $L_\infty$ and sharp estimates for discrepancy of weighted graphs and hypergraphs
AI总结：
本文证明多重 Rademacher 系统与 Rademacher 混沌在 $L_\infty$ 中具有随机无条件收敛性，并据此建立边加权图与超图偏差的锐双向估计，推广了 Erdös-Spencer 经典定理。
摘要：
我们证明多重 Rademacher 系统与 Rademacher 混沌在空间 $L_\infty$ 中都具有随机无条件收敛性质。这一事实，结合这些系统元素的线性组合的 $L_\infty$-范数与其系数矩阵的某些特殊范数之间的密切联系，使我们能够对边加权图和超图的偏差建立锐利的双向估计。其中一些结果推广了 Erdös 和 Spencer 针对无权情形证明的经典定理。
英文摘要：
We prove that both multiple Rademacher system and Rademacher chaos possess the property of random unconditional convergence in the space $L_\infty$. This fact combined with some intimate connections between $L_\infty$-norms of linear combinations of elements of these systems and some special norms of matrices of their coefficients allows us to establish sharp two-sided estimates for the discrepancy of edge-weighted graphs and hypergraphs. Some of these results extend the classical theorem proved by Erdös and Spencer for the unweighted case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
