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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
2
answers
17
views
0
votes
Non-negativity of a measure
real-analysis
measure-theory
Updated February 21, 2019 10:20 AM
0
answers
2
views
0
votes
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
0
answers
6
views
0
votes
A question about Fourier transform of measures
measure-theory
fourier-analysis
representation-theory
harmonic-analysis
Updated February 21, 2019 00:20 AM
0
answers
8
views
0
votes
Prove that every set that is content zero is also measure zero.
real-analysis
measure-theory
Updated February 20, 2019 23:20 PM
2
answers
728
views
1
votes
Calculating length of sides of a half parallelogram
measure-theory
Updated February 20, 2019 23:20 PM
1
answers
12
views
0
votes
$f$ 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
1
answers
12
views
2
votes
Notation for expectation of a random variable/general Lebesgue integral
integration
random-variables
lebesgue-integral
expected-value
Updated February 20, 2019 20:20 PM
0
answers
7
views
1
votes
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
0
answers
4
views
0
votes
Sub-Gaussian and "nearly" sub-Gaussian random variables
probability-theory
moment-generating-functions
concentration-of-measure
Updated February 20, 2019 17:20 PM
0
answers
3
views
0
votes
For all $E$ and $\epsilon>0$ there is $m^*(O)<m^*(e)+\epsilon$
measure-theory
lebesgue-measure
Updated February 20, 2019 16:20 PM
1
answers
12
views
0
votes
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
0
answers
6
views
0
votes
Some property of conditional independence
probability
measure-theory
probability-theory
Updated February 20, 2019 10:20 AM
2
answers
141
views
1
votes
Show the outer measure of a union is the sum of the measures without Caratheodony
measure-theory
Updated February 20, 2019 09:20 AM
1
answers
743
views
0
votes
When is the measure of spherical cap large?
probability
convex-geometry
geometric-probability
concentration-of-measure
Updated February 20, 2019 05:20 AM
0
answers
3
views
0
votes
A property of limit supermum
real-analysis
measure-theory
Updated February 20, 2019 03:20 AM
0
answers
10
views
0
votes
Limit supremum as the biggest number satisfying certain property
real-analysis
measure-theory
Updated February 20, 2019 00:20 AM
0
answers
16
views
-1
votes
How to convert $\ kWh/m^2 $ to $\ Joule/kg$
physics
unit-of-measure
Updated February 19, 2019 19:20 PM
0
answers
5
views
0
votes
Application of Dynkin's Lemma: Why is this function measurable?
probability-theory
measure-theory
Updated February 19, 2019 17:20 PM
2
answers
193
views
2
votes
Is my attempt at proving this corollary of the LDCT correct?
analysis
measure-theory
lebesgue-integral
Updated February 19, 2019 17:20 PM
0
answers
7
views
0
votes
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
0
answers
7
views
0
votes
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
0
answers
21
views
0
votes
When strong and weak measurability coincide?
real-analysis
integration
functional-analysis
measure-theory
Updated February 19, 2019 12:20 PM
1
answers
6
views
0
votes
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
2
answers
8
views
0
votes
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
0
answers
15
views
1
votes
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
1
answers
14
views
1
votes
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
0
answers
20
views
0
votes
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
0
answers
11
views
1
votes
Question on an example function (i.e. the "tent" function)
measure-theory
lebesgue-integral
Updated February 19, 2019 00:20 AM
1
answers
22
views
0
votes
Probability measure domain
probability
measure-theory
set-theory
Updated February 18, 2019 22:20 PM
0
answers
4
views
0
votes
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
0
answers
5
views
0
votes
Measurable function - characteristic function of measuable set.
measure-theory
lebesgue-measure
Updated February 18, 2019 17:20 PM
0
answers
7
views
0
votes
Borel $\sigma$-Algebra generated by open intervall with rational end point
measure-theory
Updated February 18, 2019 14:20 PM
2
answers
10
views
0
votes
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
2
answers
7
views
2
votes
Gaussian concentration of measure, equivalent definitions
probability-theory
measure-theory
normal-distribution
concentration-of-measure
Updated February 18, 2019 14:20 PM
0
answers
4
views
0
votes
Lebesgue sigma algebra
measure-theory
lebesgue-measure
Updated February 18, 2019 13:20 PM
1
answers
15
views
1
votes
Wasserstein attains its infimum
measure-theory
optimization
concentration-of-measure
optimal-transport
Updated February 18, 2019 12:20 PM
0
answers
5
views
0
votes
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
0
answers
8
views
0
votes
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
0
answers
5
views
0
votes
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
0
answers
6
views
0
votes
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
0
answers
7
views
1
votes
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
0
answers
3
views
0
votes
Measurable functions.
lebesgue-measure
measurable-functions
Updated February 18, 2019 00:20 AM
1
answers
15
views
0
votes
Interpretation of Expected value of Random Variable
probability
probability-theory
statistics
measure-theory
probability-distributions
Updated February 17, 2019 22:20 PM
2
answers
10
views
0
votes
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
1
answers
8
views
0
votes
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
1
answers
8
views
2
votes
Define a measure from density function with symmetry
integration
measure-theory
symmetric-groups
change-of-variable
Updated February 17, 2019 20:20 PM
0
answers
15
views
0
votes
Convergence of certain integrals to $f(t)/2$
real-analysis
measure-theory
pde
Updated February 17, 2019 18:20 PM
1
answers
15
views
0
votes
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
0
answers
6
views
1
votes
Why Koopman operator is defined on $L^\infty$ space?
functional-analysis
measure-theory
operator-theory
operator-algebras
Updated February 17, 2019 15:20 PM
2
answers
23
views
1
votes
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