List questions from riemann-integration | MathQA

Define a set $S$ of finite number of distinct points, and $f(x)=1$ if $x\notin S$ and $f(x)=0$ if $x\in S$. Prove $f\in \mathcal{R}$.

Published on 18 Jan 2023 - 3:14

Proof that the Riemann-sums of $\int_0^1\tfrac{1}{x}\text{d}x$ diverge to $+\infty$

Published on 02 Apr 2026 - 3:51

Prove or disprove Riemann-integrability (I guess there are uncountably many points of discontinuity)

Published on 25 Jan 2023 - 23:05

Prove there is no bounded function $\rho\in \mathcal{R}$ on $[-1,1]$ such that $\int_{-1}^1 f(x)\rho(x) dx=f(0)$ for every continuous $f$ on $[-1,1]$

Published on 27 Jan 2023 - 7:23