A note on the almost sure central limit theorem for some dependent random variables

A percolation problem on Sierpinski carpet lattices is considered. It is obtained that the critical probability (p) over{rightarrow of oriented percolation is equal to 1. In contrast it was already shown that the critical probability pc of percolation is strictly less than 1 in Kumagai [9]. This result shows a difference between fractal-like lattice and Zd lattice.