R. Pyke raised the question of the convergence of series indexed by filtering sets. This paper contains a generalization of an inequality of Marcinkiewicz-Zygmund for a certain class of filtering sets, which gives rise to the theory of series for this type of set.
"An Inequality for Sums of Independent Random Variables Indexed by Finite Dimensional Filtering Sets and Its Applications to the Convergence of Series." Ann. Probab. 5 (5) 779 - 786, October, 1977. https://doi.org/10.1214/aop/1176995719