New posts in real-analysis

Definition of completion of a measure space

real-analysis measure-theory

Simplify $\sum_{l=0}^\infty \sum_{r=0}^\infty\frac{\Gamma(L+r-2q)}{\Gamma(L+r-1+2q)} \frac{\Gamma(L+r+l-1+2q)}{\Gamma(L+r+l+2)}\frac{r+1}{r+l+2}$

real-analysis sequences-and-series special-functions hypergeometric-function

Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable.

real-analysis analysis measure-theory

Closed form for $\int x^ne^{-x^m} \ dx\ ?$

calculus real-analysis gamma-function

Reference request for CMI M.Sc entrance exam

real-analysis abstract-algebra general-topology complex-analysis reference-request

Does $f'(x)>0$ a.e. imply that $f$ is strictly monotone?

Is uniform continuity related to the rate of change of the function?

real-analysis soft-question intuition uniform-continuity

$n^3+n<3^n$ for $n \geq4$ by induction.

calculus real-analysis number-theory induction

Prove or disprove that if $\lim\limits_{x\to0^+}f(x)=0$ and $|x^2f''(x)|\leq c$ then $\lim\limits_{x\to0^+}xf'(x)=0$

real-analysis limits derivatives

Prove that $a_1 \cos(b_1 x) + \dots + a_n \cos(b_n x)$ has zero

real-analysis derivatives trigonometry

Prove that between any two rational numbers there is a rational whose numerator and denominator are both perfect squares.

Evaluate $\lim\limits_{n \to \infty} nx_n.$

real-analysis calculus sequences-and-series limits

I want to find A real valued function having a continuous first derivative for all points in domain, but with undefined higher order derivatives.

real-analysis continuity

What's so special about square root cancellation?

real-analysis statistics analytic-number-theory

Counterexample to Tonelli's theorem

real-analysis integration examples-counterexamples fubini-tonelli-theorems

An interesting series related to primes satisfying $\sum_n x_{nk} = 0$ for all $k$

real-analysis sequences-and-series number-theory prime-numbers

Chicken-Egg problem with Fubini’s theorem

real-analysis measure-theory

If $x_1<x_2$ are arbitrary real numbers, and $x_n=\frac{1}{2}(x_{n-2}+x_{n-1})$ for $n>2$, show that $(x_n)$ is convergent.

real-analysis sequences-and-series recurrence-relations

limit of increasing sequence of measures is a measure

real-analysis measure-theory

Proving that $X$ is a Banach space iff convergence of $\sum\|x_n\|$ implies convergence of $\sum x_n$

real-analysis sequences-and-series functional-analysis banach-spaces normed-spaces