Newbetuts

Show that a set $A \subset \mathbb{R}^2$ of positive Lebesgue measure contains the vertices of an equilateral triangle

The completion of the Borel $\sigma$-algebra the same as the completion of the Lebesgue outer measure?

The integral of a characteristic function with respect to a product measure.

Convergence with indicator functions

Prove that $\vert E \vert=0$ if $\frac{x+y}{2}\notin E$ for $x,y \in E$

If $f\in\mathcal{M}$ then $f=\sum_{n=0}^{\infty}a_n \mathcal{X}_{A_{n}}$

How is area defined?

Intuitive Explanation of Why the Power Set of $\mathbb{R}$ is "too big" for the Lebesgue Measure?

Why is the inner measure problematic?

How to solve this estimate $m\{t \in[a, b]:|f(t)| \leq \varepsilon\} \leq 4\left(q ! \frac{\varepsilon}{2 \beta}\right)^{\frac{1}{q}}$

if $f_n\geq 0$ a.e. and $f_n\longrightarrow f$ in measure then $f\geq 0$ a.e.

Show that for any integrable function...

A set with measure $0$ has a translate containing no rational number.

Nowhere dense subsets of $[0,1]$ with positive measure other than fat Cantor sets

Geometric definitions of infinity

The exterior/outer measure of an open cube

Integral of probability density over a Borel set

New posts in lebesgue-measure

Show that a set $A \subset \mathbb{R}^2$ of positive Lebesgue measure contains the vertices of an equilateral triangle

Number of flips to get to a Set of Positive Lebesgue Measure

Measurable set of real numbers with arbitrarily small periods

Example of decreasing sequence of sets with first set having infinite measure

The completion of the Borel $\sigma$-algebra the same as the completion of the Lebesgue outer measure?

The integral of a characteristic function with respect to a product measure.

Convergence with indicator functions

Prove that $\vert E \vert=0$ if $\frac{x+y}{2}\notin E$ for $x,y \in E$

If $f\in\mathcal{M}$ then $f=\sum_{n=0}^{\infty}a_n \mathcal{X}_{A_{n}}$

How is area defined?

Intuitive Explanation of Why the Power Set of $\mathbb{R}$ is "too big" for the Lebesgue Measure?

Why is the inner measure problematic?

How to solve this estimate $m\{t \in[a, b]:|f(t)| \leq \varepsilon\} \leq 4\left(q ! \frac{\varepsilon}{2 \beta}\right)^{\frac{1}{q}}$

if $f_n\geq 0$ a.e. and $f_n\longrightarrow f$ in measure then $f\geq 0$ a.e.

Show that for any integrable function...

A set with measure $0$ has a translate containing no rational number.

Nowhere dense subsets of $[0,1]$ with positive measure other than fat Cantor sets

Geometric definitions of infinity

The exterior/outer measure of an open cube

Integral of probability density over a Borel set