Statistical \(p\)-convergence in lattice-normed Riesz spaces

A sequence \((x_n)\) in a lattice-normed space \((X,p,E)\) is statistical \(p\)-convergent to \(x\in X\) if there exists a statistical \(p\)-decreasing sequence \(q\stpd 0\) with an index set \(K\) such that \(\delta(K)=1\) and \(p(x_{n_k}-x)\leq q_{n_k}\) for every \(n_k\in K\). This convergence has been investigated recently for \((X,p,E)=(E,|\cdot|,E)\) under the name of statistical order convergence and under the name of statistical multiplicative order convergence, and also, for taking \(E\) as a locally solid Riesz space under the names statistically unbounded \(\tau\)-convergence and statistically multiplicative convergence. In this paper, we study the general properties of statistical \(p\)-convergence.