New posts in measure-theory

Extension of the Lebesgue measurable sets

real-analysis measure-theory

If a continuous function is positive on the rationals, is it positive almost everywhere?

real-analysis measure-theory examples-counterexamples

Exercise 1.6.3 from Alon & Spencer's The Probabilistic Method: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$

probability combinatorics probability-theory measure-theory inequality

What's the relationship between a measure space and a metric space?

real-analysis analysis measure-theory lebesgue-measure

Are Monotone functions Borel Measurable?

measure-theory monotone-functions measurable-functions borel-sets

Proving the scaling property of the Lebesgue measure using Dynkin's lemma

measure-theory lebesgue-measure

Is there any difference between the notations $\int f(x)d\mu(x)$ and $\int f(x) \mu(dx)$?

notation integration measure-theory

How to prove limit of measurable functions is measurable

measure-theory elementary-set-theory

Infinite product of measurable spaces

measure-theory elementary-set-theory product-space

Is there a $\sigma$-algebra on $\mathbb{R}$ strictly between the Borel and Lebesgue algebras?

real-analysis measure-theory descriptive-set-theory

Interpretation of limsup-liminf of sets

probability measure-theory elementary-set-theory limsup-and-liminf

Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$

real-analysis integration measure-theory

Limit of measures is again a measure

Convergence of integrals in $L^p$

measure-theory lp-spaces

Why do we restrict the definition of Lebesgue Integrability?

integration measure-theory improper-integrals lebesgue-integral intuition

Are vague convergence and weak convergence of measures both weak* convergence?

functional-analysis measure-theory probability-theory

Difference between topology and sigma-algebra axioms.

general-topology measure-theory soft-question

What is the difference between outer measure and Lebesgue measure?

real-analysis measure-theory lebesgue-measure

Intuition behind the definition of a measurable set

measure-theory intuition measurable-sets

If $f,g$ are measurable and $\Phi$ is continuous, then $\Phi(f(x),g(x))$ is measurable.

real-analysis measure-theory lebesgue-measure