lebesgue measure related issues & queries in MathXchanger

Sigma algebra generated by a random variable

probability probability-theory measure-theory
Updated February 21, 2019 16:20 PM

Non-negativity of a measure

real-analysis measure-theory
Updated February 21, 2019 10:20 AM

Define a Borel function on the whole space with some constraints

measure-theory set-theory descriptive-set-theory measurable-functions polish-spaces
Updated February 21, 2019 10:20 AM

A question about Fourier transform of measures

measure-theory fourier-analysis representation-theory harmonic-analysis
Updated February 21, 2019 00:20 AM

Prove that every set that is content zero is also measure zero.

real-analysis measure-theory
Updated February 20, 2019 23:20 PM

Calculating length of sides of a half parallelogram

measure-theory
Updated February 20, 2019 23:20 PM

$f$ is the pointwise limit of measurable functions $f_n$. Show $\lambda(f^{-1}(a,\infty]) \leq \liminf_{n\to \infty }\lambda(f_n^{-1}[a, \infty])$

real-analysis measure-theory lebesgue-measure
Updated February 20, 2019 22:20 PM

Notation for expectation of a random variable/general Lebesgue integral

integration random-variables lebesgue-integral expected-value
Updated February 20, 2019 20:20 PM

Let $ \Omega = \{ x \in \mathbb{R} : | x | \leq 1 \} $. Show that the function $ v(x) = |x|^{\alpha} $ belong to $ H^1(\Omega) $ if $ \alpha > 0 $

functional-analysis analysis hilbert-spaces lebesgue-integral
Updated February 20, 2019 18:20 PM

Sub-Gaussian and "nearly" sub-Gaussian random variables

probability-theory moment-generating-functions concentration-of-measure
Updated February 20, 2019 17:20 PM

For all $E$ and $\epsilon>0$ there is $m^(O)<m^(e)+\epsilon$

measure-theory lebesgue-measure
Updated February 20, 2019 16:20 PM

What are sufficient conditions for the boundedness of a Radon-Nikodym derivative of a pull back measure?

measure-theory absolute-continuity radon-nikodym
Updated February 20, 2019 10:20 AM

Some property of conditional independence

probability measure-theory probability-theory
Updated February 20, 2019 10:20 AM

Show the outer measure of a union is the sum of the measures without Caratheodony

measure-theory
Updated February 20, 2019 09:20 AM

When is the measure of spherical cap large?

probability convex-geometry geometric-probability concentration-of-measure
Updated February 20, 2019 05:20 AM

A property of limit supermum

real-analysis measure-theory
Updated February 20, 2019 03:20 AM

Limit supremum as the biggest number satisfying certain property

real-analysis measure-theory
Updated February 20, 2019 00:20 AM

How to convert $\ kWh/m^2 $ to $\ Joule/kg$

physics unit-of-measure
Updated February 19, 2019 19:20 PM

Application of Dynkin's Lemma: Why is this function measurable?

probability-theory measure-theory
Updated February 19, 2019 17:20 PM

Is my attempt at proving this corollary of the LDCT correct?

analysis measure-theory lebesgue-integral
Updated February 19, 2019 17:20 PM

Prove $A\subseteq B \subseteq \mathbb{R}\to m^(B)-m^(A)\leq m^*(B \setminus A)$

measure-theory lebesgue-measure outer-measure
Updated February 19, 2019 17:20 PM

Showing that $f*\phi_t\to af$ in $\|\cdot\|_p$ as $t\to\infty$ with $f,\phi$ as given

integration functional-analysis convergence lebesgue-integral convolution
Updated February 19, 2019 15:20 PM

When strong and weak measurability coincide?

real-analysis integration functional-analysis measure-theory
Updated February 19, 2019 12:20 PM

Given $\{f_k\}$, a sequence of bounded, complex-valued measurable functions, prove $\lim_{k \to \infty} \int_{\Omega} f_k dx = \int_{\Omega} f dx$

real-analysis sequences-and-series limits lebesgue-integral
Updated February 19, 2019 10:20 AM

Proof that makes use of the differentiability of a function and of its convex conjugate

measure-theory proof-writing convex-analysis lebesgue-measure convex-geometry
Updated February 19, 2019 09:20 AM

Upper bound for some measurable sets given the inequality $\sum_{n=1}^{\infty} \mu (A_{n}) \leq \mu (\bigcup_{n=1}^{\infty} A_{n}) + \epsilon$

real-analysis measure-theory measurable-sets
Updated February 19, 2019 08:20 AM

If $E$ has finite Lebesgue measure, then there is an $n\in \mathbb{N}$ such that $\lambda(E) = \lambda(E \cap [-n,n])$.

measure-theory lebesgue-measure
Updated February 19, 2019 03:20 AM

Suppose that $E \subset \mathbb{R}$. If $E \cap F$ is Lebesgue measurable for all measurable $F$ such that $m(F)$ is finite, then $E$ is measurable.

measure-theory lebesgue-measure
Updated February 19, 2019 01:20 AM

Question on an example function (i.e. the "tent" function)

measure-theory lebesgue-integral
Updated February 19, 2019 00:20 AM

Probability measure domain

probability measure-theory set-theory
Updated February 18, 2019 22:20 PM

If $\kappa$ is a transition kernel and $f$ is measurable, is $\int f(\;\cdot\;,\omega_2)\kappa(\;\cdot\;,{\rm d}\omega_2)$ measurable?

probability-theory measure-theory
Updated February 18, 2019 21:20 PM

Measurable function - characteristic function of measuable set.

measure-theory lebesgue-measure
Updated February 18, 2019 17:20 PM

Borel $\sigma$-Algebra generated by open intervall with rational end point

measure-theory
Updated February 18, 2019 14:20 PM

Questions on the proof of $f*g\in C^\infty(\mathbb R)$ when $f\in L^2(\mathbb R)$ and $g\in C_c^\infty(\mathbb R)$

calculus measure-theory derivatives lebesgue-integral convolution
Updated February 18, 2019 14:20 PM

Gaussian concentration of measure, equivalent definitions

probability-theory measure-theory normal-distribution concentration-of-measure
Updated February 18, 2019 14:20 PM

Lebesgue sigma algebra

measure-theory lebesgue-measure
Updated February 18, 2019 13:20 PM

Wasserstein attains its infimum

measure-theory optimization concentration-of-measure optimal-transport
Updated February 18, 2019 12:20 PM

Define a Borel function on the whole space - Self study

measure-theory elementary-set-theory descriptive-set-theory measurable-functions polish-spaces
Updated February 18, 2019 10:20 AM

Integrating continuous function of two variables by one of the variables, do I get continuous function?

integration continuity lebesgue-integral riemann-integration
Updated February 18, 2019 09:20 AM

Lebesgue measure, there exists a measurable subset $E_t\subset E$ with $m(E_t) = t$.

real-analysis lebesgue-measure
Updated February 18, 2019 05:20 AM

A problem from Folland: constructing Haar measure from Lebesgue measure

real-analysis analysis measure-theory harmonic-analysis haar-measure
Updated February 18, 2019 03:20 AM

Bounds for the derivative of inverse Mills ratio of standard normal distribution

probability-theory measure-theory probability-distributions normal-distribution
Updated February 18, 2019 00:20 AM

Measurable functions.

lebesgue-measure measurable-functions
Updated February 18, 2019 00:20 AM

Interpretation of Expected value of Random Variable

probability probability-theory statistics measure-theory probability-distributions
Updated February 17, 2019 22:20 PM

For every Lebesgue measure set $E,$ the map $x\mapsto\overline{\lambda}(E\cap(E+x))$ is continuous

measure-theory lebesgue-measure
Updated February 17, 2019 22:20 PM

Apply the Monotone Convergence Theorem to show that λ is countably additive.

analysis measure-theory convergence lebesgue-integral
Updated February 17, 2019 21:20 PM

Define a measure from density function with symmetry

integration measure-theory symmetric-groups change-of-variable
Updated February 17, 2019 20:20 PM

Convergence of certain integrals to $f(t)/2$

real-analysis measure-theory pde
Updated February 17, 2019 18:20 PM

Finitely Additive Homogeneous Translation Invariant Measure on $\mathcal{P}(\mathbb{R})$

real-analysis functional-analysis measure-theory hahn-banach-theorem
Updated February 17, 2019 16:20 PM

Why Koopman operator is defined on $L^\infty$ space?

functional-analysis measure-theory operator-theory operator-algebras
Updated February 17, 2019 15:20 PM

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