sentences:  Consider a metric space ("X", "d") and a subset "E" of "X".Given a number "s" ≥ 0, the "s"-dimensional Hausdorff measure of "E", denoted "μ""s"("E"), is defined by
  
  where
  
  "μ""δ""s"("E") can be thought of as an approximation to the "true" "s"-dimensional area/volume of "E" given by calculating the minimal "s"-dimensional area/volume of a covering of "E" by sets of diameter at most "δ".As a function of increasing "s", "μ""s"("E") is non-increasing.