Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces. (15th April 2018) - Xue, Xuemei; Tao, Jian
Abstract : A new concept of statisticallye -uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statisticallye -uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence.