We prove a Marstrand type slicing theorem for the subsets of the integer square lattice. This problem is the dual of the corresponding projection theorem, which was considered by Glasscock, and Lima and Moreira, with the mass and counting dimensions applied to subsets of Z d . In this paper, more generally we deal with a subset of the plane that is 1 separated, and the result for subsets of the integer lattice follow as a special case. We show that the natural slicing question in this setting is true with the mass dimension.Recently there have been two proofs of this celebrated conjecture [6, 9].(2) We could in principle consider an arbitrary point set in R 2 , but when we have some limit points in our set, then the dimension of the set goes to infinity. For 1-separated sets in the plane, the dimension is at most 2.

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