sentences:  Almost surely, a sample path "X" of Brownian motion in the Euclidean plane has Hausdorff dimension equal to 2, but the 2-dimensional Hausdorff measure "μ"2("X") is zero.The exact dimension function "h" is given by the logarithmic correction
  
  I.e., with probability one, 0 "h"("X") 2.For Brownian motion in Euclidean "n"-space R"n" with "n" ≥ 3, the exact dimension function is