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In this paper, we extend some results concerning statistical convergence in locally solid Riesz spaces by introducing a more general idea of convergence, namely I λ -statistical convergence. We investigate the ideas of I λ -statistical-τ-convergence, I λ -statistical-τ-boundedness and I λ -statistical-τ-Cauchy condition of sequences in a locally solid Riesz space endowed with a topology τ and investigate some of their consequences.

On I λ -Statistical Convergence in Locally Solid Riesz Spaces