Course Details
Country:
Netherlands
Institution:
Free University of Amsterdam
Course Title:
Measure Theory
Course Number:
X_401028
Course Description:
We motivate and introduce the notion of a measure, that is, a way to assign a size to as many subsets as possible in an abstract space. It turns out that it is in general not possible to measure all sets, at least if one insists on countable additivity of the measure. This leads to the notion of a sigma-algebra. We show how one can obtain a unique measure on a sigma algebra once certain basic properties are imposed. Once we have defined measure, we can introduce and discuss so called measurable functions which, roughly speaking, form the class of functions which we will be able to integrate. We then introduce and study integration of these measurable functions with respect to a measure. We discuss (among other things) the monotone and dominated convergence theorems concerning the interchangeability of limit and integral, the substitution rule, and more.
Language:
English
Approved Equivalent:
Pending For Approval
Attachment Files:
Studyguide (15)_1.pdf
