New posts in real-analysis

Show that $(x_{n})_{n}$ is dense in $[0,1]\setminus A$ then it is also dense in $[0,1]$

Lebesgue space and weak Lebesgue space

Exercise about continuous functions

Diffeomorphism-invariant spaces of smooth functions

Does a glass of water sing because of the SO(2) symmetry?

Prove that the equation $x^2=y$ has a unique solution

Baby Rudin 1.14 is essentially Thales's theorem?

Is the function $A \mapsto \sum\limits_{j=0}^{\infty} \langle A^j v, A^j v \rangle$ differentiable everywhere?

Study continuity of $f(x) = |x|$ for $x\in\Bbb R \setminus \Bbb Q$, $f(x) = \frac{qx}{q+1}$ for $x\in\Bbb Q$.

Mean Value Theorem Integrals

A reason for $ 64\int_0^1 \left(\frac \pi 4+\arctan t\right)^2\cdot \log t\cdot\frac 1{1-t^2}\; dt =-\pi^4$ ...

German Analysis Texts

The set of discontinuous points is countable union of closed sets

Why is a strictly monotonic mapping between intervals continuous?

How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?

Supremum of subsequences

Showing that all monotone functions are integrable

Convergence of sequence in the limit points of a sequence

Understanding the class of all convergent sequences in a discrete space. [duplicate]

Nowhere continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f(f(x)) = (f(x))^2$