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.

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

The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …
Last updated on 3 min read expository