For a Radon probability measure μ on ℝn we can use the Hausdorff dimension dimH and the packing dimension dimp to define lower indices

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and

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For two such measures μ and ν intersection measures μ ∩ f# ν are obtained by slicing a certain product measure on ℝn × ℝn using diagonal n-planes, and by projecting the result onto ℝn. Here f is a similarity on ℝn and f# ν is the image of the measure ν under f. Our main result gives a lower bound for the packing dimension of these intersection measures under the condition dimH μ+dimH ν > n and some additional assumptions.