6 problems.
- \(f_n(x)=x/(1+nx^2)\) converges uniformly, but \(f'=\lim f_n'\) fails at \(0\)
- \(\int_0^x e^{t^2}\,dt>\frac{x^2}{2}+\ln(1+x)\) for small \(x\)
- A measurable set of measure \(p\) meets \([0,x]\) in every measure \(c\in[0,p)\)
- Integrability of \(\sin\circ f\) and a Fubini identity for nonnegative integrable \(f\)
- An absolutely continuous function with \(f'\in L^p\) is Hölder continuous of exponent \((p-1)/p\)
- Absolutely continuous functions on \([0,1]\) form a Banach space under \(\|f\|_1+\|f'\|_1\)