New posts in measure-theory

Two definitions of Lebesgue integration

real-analysis measure-theory

What is the relation between weak convergence of measures and weak convergence from functional analysis

functional-analysis measure-theory probability-theory

The set of convergence of a sequence of measurable functions is measurable

measure-theory convergence-divergence

Pre-image of a measurable set A is always measurable?

real-analysis measure-theory

Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.

real-analysis measure-theory vector-spaces lebesgue-measure geometric-measure-theory

Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick

real-analysis probability-theory measure-theory borel-cantelli-lemmas

Lebesgue density theorem in the line

real-analysis measure-theory lebesgue-measure

Uniqueness of product measure (non $\sigma$-finite case)

real-analysis measure-theory probability-theory examples-counterexamples

Showing that rationals have Lebesgue measure zero.

Properties of the functions $f(x-t)$ for $t \in \mathbb{R}$

real-analysis measure-theory lp-spaces

Vitali set of outer-measure exactly $1$.

real-analysis measure-theory lebesgue-measure

Is $(f\mapsto\int_\Omega f d\mu)\in L^1(\Omega,\lambda)^*$?

Haar Measure of a Topological Ring

measure-theory reference-request representation-theory topological-groups topological-rings

Metric assuming the value infinity

measure-theory metric-spaces

What is the Kolmogorov Extension Theorem good for?

probability measure-theory stochastic-processes

Difference between Modification and Indistinguishable

measure-theory probability-theory stochastic-processes

When exactly is the dual of $L^1$ isomorphic to $L^\infty$ via the natural map?

analysis functional-analysis measure-theory lp-spaces

Cartesian product of two collections of sets?

probability-theory measure-theory

Prove that/Explain how for independent random variables $X_i$, we have $f_i(X_i)$ are independent (in particular without measure theory)

probability probability-theory measure-theory independence moment-generating-functions

Folland, "Real Analysis", Chapter 5.3, Exercise 36.

real-analysis functional-analysis measure-theory