New posts in almost-everywhere

If $\int_A f\,dm = 0$ for all $A$ having some fixed measure $C$, then $f = 0$ almost everywhere

real-analysis analysis measure-theory lebesgue-integral almost-everywhere

If $ \int fg = 0 $ for all compactly supported continuous g, then f = 0 a.e.?

real-analysis functional-analysis lebesgue-integral lebesgue-measure almost-everywhere

Why do we need to define Lebesgue spaces using equivalence classes?

functional-analysis equivalence-relations almost-everywhere

If X and Y are equal almost surely, then they have the same distribution, but the reverse direction is not correct

probability-theory measure-theory probability-distributions random-variables almost-everywhere

Proving $n^{-1/2}\sum_{k=1}^{n}a_{nk}X_k\to0$ a.s

probability-theory almost-everywhere

Proving $\frac{1}{n} \sum_{k=1}^{n}X_{k}\to 0$ a.s.

probability-theory borel-cantelli-lemmas almost-everywhere

Almost Everywhere Convergence versus Convergence in Measure

real-analysis measure-theory convergence-divergence almost-everywhere

Lipschitz continuity implies differentiability almost everywhere.

derivatives lipschitz-functions almost-everywhere

Measurability of an a.e. pointwise limit of measurable functions.

measure-theory convergence-divergence almost-everywhere

$\int_0^1f(t)\phi'(t)dt=-\int_0^1g(t)\phi(t)dt$, for all smooth $\phi\in[0,1]$ implies $f$ is absolutely continuous and $f'=g$ a.e.

real-analysis derivatives lebesgue-integral almost-everywhere absolute-continuity