On Lacunary double statistical convergence in locally solid Riesz spaces

The concept of statistical convergence is one of the most active area of research in the field of summability. Most of the new summability methods have relation with this popular method. In this paper, we introduce the concept of double $\theta$- statistical-$\tau$- convergence which is more general idea of convergence. We also investigate the ideas of double $I_{\theta}$-statistical-$\tau$-boundedness and double $I_{\theta}$-statistical-$\tau$- Cauchy condition of sequences in framework of locally solid Riesz space endowed with a topology $\tau$ and investigate some of their consequences