fix: some minor mistakes

[infmagic2047]

Fix some mistakes I discovered while reading.

1. Frobenius determinant: from online sources I have seen definitions of the Frobenius determinant using $x_{gh}$, $x_{gh^{-1}}$, or $x_{g^{-1}h}$. However, I believe the $x_{gh^{-1}}$ definition is needed to make the example (b) correct (it has a sign error now), and to make $T = \sum_{g \in G} x_g \rho(g)$ in the proof work.
2. Cauchy mean value theorem: this form of the theorem does not need $g(a) \neq g(b)$.
3. Power series of holomorphic functions: add the missing $\frac{1}{2\pi i}$ factors.
4. Problem 36B: I think the measurable sets would be just $\varnothing$ and $\Omega$, as for any other set $A$ we can pick $E$ with one point from $A$ and one point from $\Omega \setminus A$.
5. Lebesgue integration: move a precondition to the right place.
6. Example 38.1.4: I think $\mathbf{1}_{(k, \infty)}$ is the intended function.

[vEnhance]

thanks much!