Newbetuts

If $p$ is a non-zero real polynomial then the map $x\mapsto \frac{1}{p(x)}$ is uniformly continuous over $\mathbb{R}$

Sum of a rearranged alternating harmonic series, with three positive terms followed by one negative term

For any unbounded set of real numbers, is there a subset which almost coincides with a uniformly spread out set of points an infinite amount of times?

Connected subsets of set

Integral $\int_0^\infty \log \frac{1+x^3}{x^3} \frac{x \,dx}{1+x^3}=\frac{\pi}{\sqrt 3}\log 3-\frac{\pi^2}{9}$

Prove that limit inferior is same as limit superior for a convergent sequence

For any given function $f\colon [0,1]\to\Bbb R$, what is $\int_0^1\frac{f(x)}{f(x)+f(1-x)}dx$?

A function that is bounded and measurable but not Lebesgue integrable

If $\ \sum_{k=1}^n m(E_n) > n-1,$ then prove that $\bigcap_{k=1}^n E_k$ has positive measure.

Strictly convex if and only if derivative strictly increasing?

Vitali Covering theorem, countable sub-collection?

$f_n(x_n) \rightarrow f(x) $ by uniform convergence

Under which conditions a solution of an ODE is analytic function?

Equivalent Topologies

Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$

New posts in real-analysis

Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.

$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$

Prove that $\int_E |f_n-f|\to0 \iff \lim\limits_{n\to\infty}\int_E|f_n|=\int_E|f|.$

Is this proof for the limit law of the product of converging sequences correct? [duplicate]

subdifferential rule proof

If $p$ is a non-zero real polynomial then the map $x\mapsto \frac{1}{p(x)}$ is uniformly continuous over $\mathbb{R}$

Sum of a rearranged alternating harmonic series, with three positive terms followed by one negative term

For any unbounded set of real numbers, is there a subset which almost coincides with a uniformly spread out set of points an infinite amount of times?

Connected subsets of set

Integral $\int_0^\infty \log \frac{1+x^3}{x^3} \frac{x \,dx}{1+x^3}=\frac{\pi}{\sqrt 3}\log 3-\frac{\pi^2}{9}$

Prove that limit inferior is same as limit superior for a convergent sequence

For any given function $f\colon [0,1]\to\Bbb R$, what is $\int_0^1\frac{f(x)}{f(x)+f(1-x)}dx$?

A function that is bounded and measurable but not Lebesgue integrable

If $\ \sum_{k=1}^n m(E_n) > n-1,$ then prove that $\bigcap_{k=1}^n E_k$ has positive measure.

Strictly convex if and only if derivative strictly increasing?

Vitali Covering theorem, countable sub-collection?

$f_n(x_n) \rightarrow f(x) $ by uniform convergence

Under which conditions a solution of an ODE is analytic function?

Equivalent Topologies

Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$