The statistically unbounded $τ$-convergence on locally solid Riesz spaces

A sequence $(x_n)$ in a locally solid Riesz space $(E,τ)$ is said to be statistically unbounded $τ$-convergent to $x\in E$ if, for every zero neighborhood $U$, $\frac{1}{n}\big\lvert\{k\leq n:\lvert x_k-x\rvert\wedge u\notin U\}\big\rvert\to 0$ as $n\to\infty$. In this paper, we introduce this concept and give the notions $st$-$u_τ$-closed subset, $st$-$u_τ$-Cauchy sequence, $st$-$u_τ$-continuous and $st$-$u_τ$-complete locally solid vector lattice. Also, we give some relations between the order convergence and the $st$-$u_τ$-convergence.

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