Newbetuts
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New posts in measure-theory
Nearly, but not almost, continuous
real-analysis
measure-theory
Is there an example of a sigma algebra that is not a topology?
general-topology
measure-theory
examples-counterexamples
If $\mathcal{B}$ is a base of a topology space $\left(X,\tau\right)$, then the Borel $\sigma$-algebra is generated by $\mathcal{B}$?
general-topology
measure-theory
lebesgue-measure
Solution verification: $m(A)>1$ implies $\exists x,y\in A$ s.t. $x-y\in\mathbb{N}.$
real-analysis
integration
measure-theory
solution-verification
lebesgue-measure
Formally show that the set of continuous functions is not measurable
general-topology
measure-theory
Is a random variable constant iff it is trivial sigma-algebra-measurable?
real-analysis
probability-theory
measure-theory
constants
Each atom of the measure μ is equivalent to a singleton.
probability-theory
measure-theory
solution-verification
proof-explanation
Can we think of the Fourier series as a Bochner integral?
measure-theory
fourier-series
Any lower semicontinuous function $f: X \to \mathbb{R}$ on a compact set $K \subseteq X$ attains a min on $K$.
measure-theory
semicontinuous-functions
Does a continuous and 1-1 function map Borel sets to Borel sets?
real-analysis
measure-theory
descriptive-set-theory
Why is the Monotone Convergence Theorem restricted to a nonnegative function sequence?
real-analysis
integration
measure-theory
lebesgue-integral
lebesgue-measure
Measure theoretic definition of curl
measure-theory
differential-geometry
geometric-measure-theory
Every non-measurable $X \subseteq \mathbb{R}^n$ has non-measurable $Y \subseteq X$ such that $|Z|=0$ for every measurable $Z \subseteq Y$
measure-theory
lebesgue-measure
Is $p$-norm decreasing in $p$?
measure-theory
probability-theory
banach-spaces
Reconciling several different definitions of Radon measures
real-analysis
functional-analysis
measure-theory
Differentiation under the integral sign for Lebesgue integrable derivative
real-analysis
analysis
measure-theory
lebesgue-integral
leibniz-integral-rule
A snappy proof of Fatou's lemma
real-analysis
measure-theory
reference-request
lebesgue-integral
alternative-proof
Why is expectation defined by $\int xf(x)dx$?
measure-theory
probability-theory
lebesgue-integral
Number of elements in a finite $\sigma$-algebra
real-analysis
measure-theory
Proving that a trivial product sigma algebra is the product of sigma algebras
real-analysis
measure-theory
lebesgue-measure
measurable-sets
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