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Measure-theory
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
lebesgue-integral
real-analysis
lebesgue-measure
measure-theory
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
general-topology
abstract-algebra
real-analysis
lebesgue-measure
measure-theory
Show that a $\pi$-system that is also a $d$-system is a $\sigma$-algebra.
August 1st, 2022
measure-theory
Lebesgue/Jordan null set
August 1st, 2022
measure-theory
Prove $f(x)=1/x$ is Borel measurable
April 11th, 2020
measure-theory
general-topology
Expected value of "different" probability measures
September 22nd, 2020
measure-theory
probability-theory
Limit of Sum of Cauchy Random Variables
August 1st, 2022
probability
measure-theory
probability-theory
probability-distributions
normal-distribution
Almost surely constant
March 20th, 2020
probability
measure-theory
Constant functions are measurable
November 24th, 2020
real-analysis
solution-verification
measure-theory
Approximating simple functions by step functions almost uniformly
August 1st, 2022
approximation
real-analysis
measure-theory
Convolution of L1 & L2 function: definition
May 20th, 2020
measure-theory
fourier-analysis
Cardinality of a finite $\sigma$-algebra
August 1st, 2022
probability
measure-theory
Indicator function, $\sigma$-algebra.
August 1st, 2022
general-topology
elementary-set-theory
measure-theory
real-analysis
lebesgue-integral
Fatou's lemma Proof
February 27th, 2020
measure-theory
sigma field generated by two random variables
August 1st, 2022
measure-theory
probability-theory
Holder's inequality
July 28th, 2020
real-analysis
inequality
measure-theory
limsup liminf of sequence of sets
February 19th, 2020
elementary-set-theory
limsup-and-liminf
measure-theory
Strictly increasing continuous functions map Borel sets to Borel sets
December 9th, 2020
measure-theory
real-analysis
Real analysis: collection of sets - sigma-algebra or not?
April 16th, 2020
measure-theory
real-analysis
Limits of infimum and supremum for sequences of functions
August 1st, 2022
real-analysis
limsup-and-liminf
measure-theory
Interchanging the order of limit and expectation
March 17th, 2020
measure-theory
probability-theory
random-variables
is Lebesgue measure continuous?
August 1st, 2022
measure-theory
Proof of uniqueness of the extension in Kolmogorov extension theorem
August 1st, 2022
probability-theory
measure-theory
Tail sigma field
August 1st, 2022
measure-theory
probability-theory
If a sequence of random matrices converge in probability, do their elements also converge?
October 12th, 2020
measure-theory
random-matrices
probability-theory
statistics
Associativity of Product Sigma Algebra
December 4th, 2020
measure-theory
real-analysis
Why an integral does not exist?
August 1st, 2022
real-analysis
measure-theory
Cantor Set is closed, uncountable and has measure zero
May 15th, 2020
measure-theory
cantor-set
real-analysis
Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
November 6th, 2020
measure-theory
real-analysis
Approximation of Lebesgue-integrable functions by continuous functions.
March 23rd, 2020
measure-theory
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