# 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.

### Some Notes on Weighted Sobolev Spaces

Embedding theorems for Weighted Sobolev Spaces

### The Second Mean Value Theorem for Integrals

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

### Integration Theories

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 …

### Moore-Osgood Theorem

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

### A Weighted/Interpolated Young's Inequality

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

### The Translation Action on Function Spaces

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

### Some Periodic Functions

Some non-intuitive facts about periodic functions

### An Elementary Proof of Young's Inequality

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

### Joris' Theorem

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 …

### A Better Estimate of Kempner's Series

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