New posts in measure-theory

Kakutani skyscraper is infinite

measure-theory probability-theory dynamical-systems ergodic-theory

$(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$

measure-theory lebesgue-integral

Measure theory convention that $\infty \cdot 0 = 0$

real-analysis measure-theory

Is there a countable cover of $\mathbb{R}^2$ by balls $B(x_n, n^{-1/2})$?

real-analysis measure-theory real-numbers

Extension of measure to non measurable sets

Integral of Function in $L^p(E)$ Times Functions in Dense Set Being $0$ Implies Function is $0$

real-analysis measure-theory lp-spaces holder-inequality

Is this a good argument on what makes the Lebesgue integral more general than the Riemann integral?

real-analysis measure-theory

Is $L^{p}$ space with alternate norm Banach?

For an outer measure $m^$, does $m^(E\cup A)+m^(E\cap A) = m^(E)+m^*(A)$ always hold?

Is there any good text introducing a part of Borel-hierarchy which is in need in measure theory

measure-theory elementary-set-theory reference-request book-recommendation borel-sets

Minkowski Dimension of Special Cantor Set

real-analysis analysis measure-theory fractals cantor-set

Convergence in $L^p$ of $f_n$ implies convergence in $L^1$ of $|f_n|^p$ and $f_n^p$

real-analysis measure-theory

Definition of the total variation distance: $ V(P,Q) = \frac{1}{2} \int |p-q|d\nu$?

probability probability-theory measure-theory

Dumb question: Computing expectation without change of variable formula

probability-theory measure-theory reference-request expectation uniform-distribution

Prove that $\int f\ d\lambda = \int_{a}^{b} f(x)\ dx,$ for any $f \in \mathcal R[a,b].$

integration measure-theory proof-explanation lebesgue-integral riemann-integration

$L^p$-space convergence

real-analysis measure-theory convergence-divergence

What's the relationship between Borel set and set whose boundary is measure zero?

real-analysis measure-theory

Help needed to understand a theorem from measure theory: Approximation by really simple functions

Why does the Continuum Hypothesis make an ideal measure on $\mathbb R$ impossible?

real-analysis measure-theory examples-counterexamples

Show that there is an $F_\sigma$ set $F$ and $G_\delta$ set $G$ such that $F \subseteq E \subseteq G \text{ and } m^(F)=m^(E)=m^*(G).$ [duplicate]

real-analysis analysis measure-theory lebesgue-measure outer-measure