New post in Measure-theory

Let $f:[0,1] \to \mathbb{R}$ be given by $f(x)=0$ if $x$ rational and if $x$ is irrational , then $f(x)=9^n$

January 4th, 2023

the $\sigma$ algeba generated by the class of open intervals with rational end points coincide with the borel $\sigma$ algebra on the real line.

September 29th, 2022

Show that a $\pi$-system that is also a $d$-system is a $\sigma$-algebra.

August 1st, 2022

Lebesgue/Jordan null set

August 1st, 2022

Prove $f(x)=1/x$ is Borel measurable

April 11th, 2020

Expected value of "different" probability measures

September 22nd, 2020

Limit of Sum of Cauchy Random Variables

August 1st, 2022

Almost surely constant

March 20th, 2020

Constant functions are measurable

November 24th, 2020

Approximating simple functions by step functions almost uniformly

August 1st, 2022

Convolution of L1 & L2 function: definition

May 20th, 2020

Cardinality of a finite $\sigma$-algebra

August 1st, 2022

Indicator function, $\sigma$-algebra.

August 1st, 2022

Fatou's lemma Proof

February 27th, 2020

sigma field generated by two random variables

August 1st, 2022

Holder's inequality

July 28th, 2020

limsup liminf of sequence of sets

February 19th, 2020

Strictly increasing continuous functions map Borel sets to Borel sets

December 9th, 2020

Real analysis: collection of sets - sigma-algebra or not?

April 16th, 2020

Limits of infimum and supremum for sequences of functions

August 1st, 2022

Interchanging the order of limit and expectation

March 17th, 2020

is Lebesgue measure continuous?

August 1st, 2022

Proof of uniqueness of the extension in Kolmogorov extension theorem

August 1st, 2022

Tail sigma field

August 1st, 2022

If a sequence of random matrices converge in probability, do their elements also converge?

October 12th, 2020

Associativity of Product Sigma Algebra

December 4th, 2020

Why an integral does not exist?

August 1st, 2022

Cantor Set is closed, uncountable and has measure zero

May 15th, 2020

Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists

November 6th, 2020

Approximation of Lebesgue-integrable functions by continuous functions.

March 23rd, 2020