To understand the ‘why’ and ‘what’ of measure theory, a good place to start is to take a relook at the idea of Riemann integration that one learns in a basic calculus course. Suppose we are given a real-valued function f on a closed bounded interval [a, b]. For the sake of simplicity, let us assume that \(f\ge 0\) . If you draw the graph of this function, then it will be a curve lying above the x-axis. The issue that integration theory in calculus is built upon is to find the area of the region enclosed under the curve between \(x=a\) and \(x=b\) . Of course, the answer to the problem is easy when f is a constant function (in which case the enclosed region would be a rectangle) or, more generally, when the graph of f is a straight line (in which case the region would be a trapezium). In both cases, school geometry provides simple formulae for these areas.