Real Analysis

Real analysis is the modern generalization of differential and integral calculus. This tag contains posts on calculus, measure theory, geometry and topology of Euclidean spaces.

The goal of this post is to make sense of the notion of the "product integral". Typically this is described with the analogy: …
9 min read Expository

At its roots, mathematical analysis is a field about existence of things that may or may not be. Fundamentally this is rooted in our …
Last updated on 19 min read expository

A fundamental result in measure theory is Egorov's Theorem, which says that if a sequence of measurable functions converge point-wise, …
Last updated on 11 min read mathematical diversions

Embedding theorems for Weighted Sobolev Spaces
Last updated on 8 min read Expository

This post concerns the second mean value theorem for definite integrals. Theorem    [Second MVT for Integrals] Let $w$ be a …
Last updated on 4 min read expository

Since I am preparing to teach intro real analysis this fall, it is a good time for me to get reacquainted with Riemann integration and …
Last updated on 8 min read expository

This short post aims at proving a general version of the Moore-Osgood Theorem on interchanging of limits. Theorem   …
Last updated on 2 min read expository

A follow up to my previous post on Young's inequality.
Last updated on 10 min read expository

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …
Last updated on 6 min read expository

Some non-intuitive facts about periodic functions
Last updated on 4 min read mathematical diversions