  A lacunary sequence is an increasing integer sequence $\theta=(k_r)$ such
that $k_r-k_{r-1}\rightarrow \infty$ as $r\rightarrow \infty.$ In this article
we introduce arithmetic statistically convergent sequence space $ASC$ and
lacunary arithmetic statistically convergent sequence space $ASC_{\theta}$ and
study some inclusion properties between the two spaces. Finally we introduce
lacunary arithmetic statistical continuity and establish some interesting
results.
