LetXbead-dimensionalrandomvectorwithunknowndensityfunctionf(z)=f(z1,···,zd),andletfnbetehnearestneighborestimatoroffproposedbyLoftsgaardenandQuesenberry(1965).Inthispaper,weestablishedthelawoftheiteratedlogarithmoffnforgeneralcaseofd≥1,whichgivestheexactpointwisestrongconvergencerateoffn.