Newbetuts
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New posts in measure-theory
metric and measure on the projective space
general-topology
measure-theory
metric-spaces
geometric-measure-theory
What's the difference between a random variable and a measurable function?
measure-theory
probability-theory
random-variables
Compute Lebesgue measure of set of all real numbers in $[0,1]$ whose decimal representations don't contain the number 7 [duplicate]
real-analysis
measure-theory
elementary-set-theory
lebesgue-measure
decimal-expansion
Proving a sufficient and necessary condition for $f:\, X\to\mathbb{R}\cup\{\pm\infty\}$ to be measurable
real-analysis
measure-theory
definition of "weak convergence in $L^1$"
probability
analysis
measure-theory
probability-theory
weak-convergence
Is there any $F \in \mathscr{F}$ such that $\mu(F)=x$?
probability
probability-theory
measure-theory
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
real-analysis
measure-theory
Let $m$ be Lebesgue measure and $a \in R$. Suppose that $f : R \to R$ is integrable, and $\int_a^xf(y) \, dy = 0$ for all $x$. Then $f = 0$ a.e.
real-analysis
measure-theory
lebesgue-integral
lebesgue-measure
$\sigma$-algebra of independent $\sigma$-algebras is independent
probability-theory
measure-theory
independence
$f$ has a zero integral on every measurable set. Prove $f$ is zero almost everywhere
probability-theory
measure-theory
lebesgue-integral
Prove that if a particular function is measurable, then its image is a rect line [duplicate]
measure-theory
functional-equations
Is there a probability measure on $[0,1]$ with no subsets with measure $\frac{1}{2}$?
real-analysis
functional-analysis
probability-theory
measure-theory
descriptive-set-theory
How to show the solution so this Fredholm integral is unique?
functional-analysis
measure-theory
operator-theory
integral-equations
How to define a p.d.f when the c.d.f is discontinuous at infinitely many points.
probability-theory
measure-theory
probability-distributions
The measure of the image of a set of measure zero
analysis
measure-theory
Isomorphic embedding of $L^{p}(\Omega)$ into $L^{p}(\Omega \times \Omega)$?
functional-analysis
measure-theory
functions
integration
banach-spaces
A problem in Sigma algebra
measure-theory
Quotient of measurable functions is measurable
real-analysis
measure-theory
Proving that the smooth, compactly supported functions are dense in $L^2$.
functional-analysis
measure-theory
lp-spaces
If $m^*([-n,n] \cap E) + m^*([-n,n] \setminus E) = 2n$ for all $n$, then $E$ is Lebesgue measurable
analysis
measure-theory
lebesgue-measure
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