Newbetuts

Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$

Regular open set whose boundary has nonzero volume.

Weird subfields of $\Bbb{R}$

Interplay of Hausdorff metric and Lebesgue measure

Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent [duplicate]

How to think about the Lebesgue measure on the Gaussian Unitary Ensemble

Why do we essentially need complete measure space?

Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$

Can sets of cardinality $\aleph_1$ have nonzero measure?

Does the graph of a measurable function always have zero measure?

Characterization of measurable sets $E$ with $|E|_e<\infty$

Measurable rectangles inside a non-null set

How to prove that $\int_{[-\pi,\pi]}\log(\vert 1- \exp(it)\vert)\mathrm{d}\lambda(t)=0$?

When does almost everywhere convergence imply convergence in measure? [duplicate]

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Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$

Regular open set whose boundary has nonzero volume.

Weird subfields of $\Bbb{R}$

Interplay of Hausdorff metric and Lebesgue measure

Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent [duplicate]

How to think about the Lebesgue measure on the Gaussian Unitary Ensemble

Why do we essentially need complete measure space?

Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$

Can sets of cardinality $\aleph_1$ have nonzero measure?

Does the graph of a measurable function always have zero measure?

Characterization of measurable sets $E$ with $|E|_e<\infty$

Measurable rectangles inside a non-null set

How to prove that $\int_{[-\pi,\pi]}\log(\vert 1- \exp(it)\vert)\mathrm{d}\lambda(t)=0$?

When does almost everywhere convergence imply convergence in measure? [duplicate]