Newbetuts

Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

If the measure of union = sum of outer measures, then the sets are measurable

problems on Lebesgue integral

Haar's theorem for the rotation-invariant distribution on the sphere

Sum of two sequences of functions converging in measure still converges in measure

Convergence to function that is not measurable

Measurability of supremum over measurable set

Why is the total variation of a complex measure defined in this way?

Linear combinations of delta measures

Lebesgue Measure of the Cartesian Product

Ergodicity of a skew product

martingale and filtration

Given a Borel set $B$ prove: for every $\epsilon$, $\exists$ compact and closed sets and a continuous $\phi$...

Equivalence of the Lebesgue integral and the Henstock–Kurzweil integral on nonnegative real functions

Prove that the normed space $L^{\infty}$ equipped with $\lVert\cdot\rVert_{\infty}$ is complete. [duplicate]

Constructing a strictly increasing function with zero derivatives

Show $\gamma(t)\leq 0$ for almost all $t$ with $\max_{u\leq t} \int_u^t \gamma \,\mathrm d\lambda = 0$

Irrationals in $[0,1]$ does not have measure zero

New posts in measure-theory

Confused about Cantor function and measure of Cantor set

Does weak convergence of measures preserve absolute continuity?

Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

If the measure of union = sum of outer measures, then the sets are measurable

problems on Lebesgue integral

Haar's theorem for the rotation-invariant distribution on the sphere

Sum of two sequences of functions converging in measure still converges in measure

Convergence to function that is not measurable

Measurability of supremum over measurable set

Why is the total variation of a complex measure defined in this way?

Linear combinations of delta measures

Lebesgue Measure of the Cartesian Product

Ergodicity of a skew product

martingale and filtration

Given a Borel set $B$ prove: for every $\epsilon$, $\exists$ compact and closed sets and a continuous $\phi$...

Equivalence of the Lebesgue integral and the Henstock–Kurzweil integral on nonnegative real functions

Prove that the normed space $L^{\infty}$ equipped with $\lVert\cdot\rVert_{\infty}$ is complete. [duplicate]

Constructing a strictly increasing function with zero derivatives

Show $\gamma(t)\leq 0$ for almost all $t$ with $\max_{u\leq t} \int_u^t \gamma \,\mathrm d\lambda = 0$

Irrationals in $[0,1]$ does not have measure zero