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.

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

A proof of a generalized form of Young's inequality is given without the need of interpolation theory.
Last updated on 6 min read expository

A proof is given of Joris' theorem, which states that if two coprime powers of a function are both smooth, then so is the original …
Last updated on 10 min read mathematical diversions