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PDF-2MATTHEWBADGERANDRAANANSCHULItisaremarkablefactthatrecti ablesetsandab PDF document

mandupperHausdor mdensity DmbyD mxliminfr0Bxr mrm201and Dmxlimsupr0Bxr mrm201forallx2RnIfD mx Dmxforsomex2RnthenwewriteDmxforthecommonvaluea

m(;)andupperHausdor m-density Dm(;)byD m(;x):=liminfr!0(B(x;r)) !mrm2[0;1]and Dm(;x):=limsupr!0(B(x;r)) !mrm2[0;1]forallx2Rn.IfD m(;x)= Dm(;x)forsomex2Rn thenwewriteDm(;x)forthecommonvaluea

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