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.

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 …

This short post aims at proving a general version of the Moore-Osgood Theorem on interchanging of limits. Theorem   …

A follow up to my previous post on Young's inequality.

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …

Some non-intuitive facts about periodic functions

A proof of a generalized form of Young's inequality is given without the need of interpolation theory.

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 …

The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …

A converse to Banach's fixed point theorem, due to Bessaga, is discussed.

Expository note on the Runge phenomenon