| Description: |
Much of modern mathematics, both pure and applied, and ranging from number theory to quantum mechanics, depends on having a method of integrating functions that applies to more functions and has better properties than the Riemann integral taught in undergraduate courses. Such a method was invented by Lebesgue; it depends on the idea of “measure'', which can be thought of as, in origin, an extension of the concepts of “area'' and “volume'', but which was subsequently seen to be precisely what is needed to found a rigorous theory of probability. The course will introduce the definition of measure, construct the most useful examples of measures, discuss integration with respect to a measure, and relate the theory to basic ideas in probability theory and functional analysis. |
