标题： 随机无条件收敛的Rademacher混沌在$L_\infty$中以及加权图和超图不一致性的精确估计 显示英文标题

标题： Random unconditional convergence of Rademacher chaos in $L_\infty$ and sharp estimates for discrepancy of weighted graphs and hypergraphs

摘要： 我们证明了多重Rademacher系和Rademacher混沌在空间$L_\infty$中都具有随机无条件收敛的性质。 这一事实结合了$L_\infty$-范数与这些系统元素的线性组合的一些特殊矩阵系数范数之间的密切联系，使我们能够建立边权图和超图差异性的精确双向估计。 其中一些结果扩展了Erdös和Spencer为无权情况证明的经典定理。 显示英文摘要

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 Erd\"os and Spencer for the unweighted case.