New posts in Measure Theory

Nontrivial Borel Sets

“Most intuitive” average of $P$ for all $x\in A \cap [a,b]$, where $A\subseteq\mathbb{R}$?

If $L^1$ average of $f$ is smaller than $t^2$ then $f=0$ a.e.

Existence of weak limit of measures

Length of a union of intervals

Minimize $q\mapsto\int\frac{(pf)^2}q\:{\rm d}\lambda$ subject to $\int q\:{\rm }\lambda=1$ using the method of Lagrange multipliers

Confusion over Motivating Example for a $\sigma$ Algebra

Doubt about Exercise 5, Chapter 1, Shakarchi [RA]

interchanging limits in something like a Riemann sum

Use Fatou Lemma to show that $f$ takes real values almost everywhere.