Math 108(b) will be principally concerned with developing the theory of Lebesgue measure. This deals with the fundamental question of how we
should think of the size of a set of real numbers.
Once we have this under control, we will develop a notion of integration which somewhat generalizes the Riemann integration which
is taught in Math 1a. By studying Lebesgue theory in this way,
in depth and from the ground up, we will gradually develop and understand some of the powerful techniques of analysis which can be
used in almost any situation. In particular, we will
study the Dominated convergence theorem and the Lebesgue differentiation theorem. We will discuss some of the far-reaching consequences
of the techniques used in proving the Lebesgue differentiation theorem.
Prerequisites: Math 108a