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.

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

This post concerns the second mean value theorem for definite integrals. Theorem [Second MVT for Integrals] Let $w$ be a …

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 …

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 …