thoughts of the Banach

With the advent of analytic geometry, however, Euclidean geometry became reinterpreted as the study of Cartesian products {{\bf R}^d} of the real line {{\bf R}}. Using this analytic foundation rather than the classical geometrical one, it was no longer intuitively obvious how to define the measure {m(E)} of a general subset {E} of {{\bf R}^d}; we will refer to this (somewhat vaguely defined) problem of writing down the