Measure theory and theory of the integral developed by Lebesgue at the beginning of the

last century found numerous applications in other branches of pure and applied mathematic for example in the theory of (partial) dierential equations, functional analysis and fractal

geometry; it is used to give mathematical foundation to probability theory and statistics, and

on the real line it gives a natural extension of the Riemann integral which allows for better

understanding of the fundamental relations between dierentiation and integration. This course

provides the essential foundations of this important aspect of mathematical analysis.