Summary
LetY i be independent stable subordinators in (ω, ℱ,P) with indices 0<β i <1 andR i are the ranges ofY i ,i=1, 2. We are able to find the exact Hausdorff measure and packing measure results for the product setsR 1×R 2, and whenever β 1 +β 2 ≦1/2, we deduce results for the vector sumR 1⊕R 2={x+y:x∈R 1,y∈R 2}.
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Hu, X. Some fractal sets determined by stable processes. Probab. Th. Rel. Fields 100, 205–225 (1994). https://doi.org/10.1007/BF01199266
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DOI: https://doi.org/10.1007/BF01199266