sentences:  In fact, for all values of "s", except possibly one, "H""s"("E") is either 0 or +∞; this exceptional value is called the Hausdorff dimension of "E", here denoted dimH("E").Intuitively speaking, "μ""s"("E") = +∞ for "s" H("E") for the same reason as the 1-dimensional linear length of a 2-dimensional disc in the Euclidean plane is +∞; likewise, "μ""s"("E") = 0 for "s" > dimH("E") for the same reason as the 3-dimensional volume of a disc in the Euclidean plane is zero.The idea of a dimension function is to use different functions of diameter than just diam("C")"s" for some "s", and to look for the same property of the Hausdorff measure being finite and non-zero.