lebesgue measure related issues & queries in MathXchanger

if $\{x| f(x) \neq g(x))\}$ has zero measure then $\int f = \int g$.

calculus measure-theory riemann-integration
Updated December 13, 2018 21:20 PM

Struggling to understand step in proof regarding a sequence of measurable functions

real-analysis measure-theory proof-explanation
Updated December 13, 2018 20:20 PM

Additive but not $\sigma$-additive function

real-analysis measure-theory probability-theory
Updated December 13, 2018 19:20 PM

Estimate w.r.t the Wasserstein Distance

probability measure-theory stochastic-calculus
Updated December 13, 2018 18:20 PM

Write $[0,1]^\mathbb{N}$ as a disjoint union of two measurable subsets such that non of which contain a cylinder.

measure-theory
Updated December 13, 2018 17:20 PM

Essential supremum of $n \sin (n^2x)$

functional-analysis lebesgue-measure norm
Updated December 13, 2018 14:20 PM

If $f(x,u(x))$ measuable with conditions

real-analysis functional-analysis measure-theory measurable-functions
Updated December 13, 2018 13:20 PM

Prove there is no map T from L0[0,1] to R satisfies that T(fn) -> 0 if and only if fn -> 0 a.e. on [0,1]

real-analysis lebesgue-measure
Updated December 13, 2018 13:20 PM

Let $U$ be a compact subset of $\mathbb{R}$ with the usual topology. Prove it's compact by sequences.

general-topology compactness real-numbers hausdorff-measure
Updated December 13, 2018 10:20 AM

An unpleasant measure theory/functional analysis problem

functional-analysis measure-theory
Updated December 13, 2018 09:20 AM

Given rectangle $L \subseteq \mathbb{R}^n$ st. $v(L) = r$, can we cover $L$ by countably many rectangles $Q_i$ s.t. $\sum_{i=1}^{\infty}v(Q_i) < r$?

real-analysis measure-theory
Updated December 13, 2018 06:20 AM

Transfering order to conditional expectation

probability-theory measure-theory hilbert-spaces conditional-expectation conditional-probability
Updated December 13, 2018 06:20 AM

Modified Boole Transformation

probability-theory measure-theory ergodic-theory
Updated December 13, 2018 04:20 AM

A function that is continuous almost everywhere is Lebesgue measurable

real-analysis analysis measure-theory lebesgue-measure
Updated December 13, 2018 02:20 AM

Fouriertransformation of bump functions

functional-analysis analysis measure-theory
Updated December 12, 2018 23:20 PM

Weak Lebesgue space

analysis lebesgue-integral weak-lp-spaces
Updated December 12, 2018 20:20 PM

Showing $f(x) = x^{-1/2}$ is Lebesgue integrable on $(0,1]$

real-analysis integration analysis lebesgue-integral
Updated December 12, 2018 20:20 PM

Why is the set $[0\le f_1\le f_2]$ measurable?

real-analysis measure-theory lebesgue-measure
Updated December 12, 2018 14:20 PM

Limits of a multiple integral function

real-analysis integration functional-analysis measure-theory lp-spaces
Updated December 12, 2018 11:20 AM

Exact value of Hausdorff measure of two dimensional Cantor set

real-analysis measure-theory fractals geometric-measure-theory hausdorff-measure
Updated December 12, 2018 09:20 AM

Image of measure is relatively compact

real-analysis measure-theory
Updated December 12, 2018 07:20 AM

$L^p$ convergence of composition

sequences-and-series analysis measure-theory convergence lp-spaces
Updated December 12, 2018 06:20 AM

Percolation Textbook Recommendation

analysis probability-theory measure-theory statistical-mechanics percolation
Updated December 12, 2018 03:20 AM

Iterated induced outermeasures from premeasure

measure-theory
Updated December 12, 2018 02:20 AM

Formally proving that the image of $f(E)$ is of measure zero when $E$ is a null set and f is $C^1$

calculus measure-theory multivariable-calculus
Updated December 12, 2018 02:20 AM

Prove that image of a continuously differential path is a null set

calculus measure-theory multivariable-calculus
Updated December 11, 2018 21:20 PM

Why can I not use this alternative, simpler way of showing that $\frac{1}{|a|}f(\frac{x-b}{a})$ is borel measurable

real-analysis probability probability-theory measure-theory
Updated December 11, 2018 20:20 PM

Support of the complex measures associated to the spectral measure

functional-analysis measure-theory spectral-theory
Updated December 11, 2018 18:20 PM

Generated \sigma-algebra contains all subsets of F?

measure-theory
Updated December 11, 2018 17:20 PM

Bounded linear maps and Lebesgue integral

functional-analysis continuity lebesgue-integral lebesgue-measure norm
Updated December 11, 2018 16:20 PM

Random variables with arbitrary positive correlation but without arbitrary negative correlation. Then $Cor(X_i,X_j)<\frac{-1}{n-1}$ not possible

probability statistics measure-theory
Updated December 11, 2018 15:20 PM

Cauchy convergence in probability implies the existence of a (finite a.e.) limit $X$

probability-theory measure-theory convergence cauchy-sequences
Updated December 11, 2018 13:20 PM

Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets

general-topology baire-category hausdorff-measure
Updated December 11, 2018 11:20 AM

Are Cat. II sets measurable (for a given outer measure)

general-topology outer-measure
Updated December 11, 2018 10:20 AM

Are Monotone functions Borel Measurable?

measure-theory
Updated December 11, 2018 08:20 AM

Convergence of pairs of random variables

probability-theory measure-theory
Updated December 11, 2018 07:20 AM

Borel measure determined uniquely on a base

real-analysis general-topology functional-analysis measure-theory geometric-measure-theory
Updated December 11, 2018 06:20 AM

Two different measures with equal support

functional-analysis measure-theory
Updated December 11, 2018 00:20 AM

Tchebyshev inequality for Measure theory.

real-analysis measure-theory lebesgue-measure
Updated December 10, 2018 23:20 PM

If $E(X_n^2)<\infty$, then for a Martingale $E(X_n^2)<M$ iff $\sum_{n=1}^\infty E[(X_n-X_{n-1})^2]<\infty$

measure-theory martingales stopping-times
Updated December 10, 2018 23:20 PM

must a measure-preserving and order-preserving bijection have measurable inverse?

real-analysis measure-theory order-theory measurable-functions
Updated December 10, 2018 23:20 PM

Calculating the norm of a specific bounded linear functional

functional-analysis lebesgue-measure lp-spaces
Updated December 10, 2018 23:20 PM

Prove that $Graph (f)=\bigcap_{n\in\mathbb N}\bigcup_{i\in\mathbb Z}f^{-1}([\frac{i}{2^n},\frac{i+1}{2^n}))\times [\frac{i}{2^n},\frac{i+1}{2^n}))$

measure-theory
Updated December 10, 2018 23:20 PM

Relation between Shannon Entropy and Total Variation distance

probability-theory measure-theory information-theory
Updated December 10, 2018 21:20 PM

Same stochastic momenta => identical distribution

probability-theory measure-theory probability-distributions
Updated December 10, 2018 21:20 PM

use $| |b|^p-|a|^p-|a-b|^p|\leq C_{p}(|a|^{p-1}|a-b|+|a||a-b|^{p-1})$ to show $\lim_{n\to \infty}\int_{X}||f_{n}|^{p}-|f|^{p}-|f-f_{n}|^{p}|d\mu=0$

real-analysis measure-theory lebesgue-measure lp-spaces
Updated December 10, 2018 20:20 PM

Equivalence of $L^p$ norm in a bounded domain

real-analysis functional-analysis measure-theory
Updated December 10, 2018 19:20 PM

Showing integrals exist but integral with respect to product measure isn't finite

measure-theory definite-integrals lebesgue-integral
Updated December 10, 2018 17:20 PM

Equivalence of the condition that the supremum of i.i.d. RVs are finite a.s.

probability-theory measure-theory random-variables independence borel-cantelli-lemmas
Updated December 10, 2018 14:20 PM

confusion about measurability requirements for Lebesgue integral

real-analysis measure-theory lebesgue-integral borel-sets
Updated December 10, 2018 14:20 PM

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