MathOverflow

Let $\mu$ be a probability measure on $\mathbb R^d$ with the Borel $\sigma$-field. Given a Borel set $A$, let $\mu^+(A)$ be its outer Minkowski content,$$\mu^+(A) = \liminf_{\varepsilon \to 0} \frac{\mu(A^\varepsilon \setminus A)}{\varepsilon},$$where...

First, I really do apologize if this is off-topic. It seems like similar things have been left up here before, so I can't really tell, and I figure it's worth a shot, because I want to hear answers from actual research mathematicians, not just the average...

The classic reference of this topic is Serre's Algebraic Groups and Class Fields. However, many parts of this book use Weil's language, which I find quite hard to follow. Is there another reference to the topic, using a more modern language (schemes...

I am studying a short-interval increment of a summatory function defined via the Dirichlet series\begin{equation}\Phi(s)=\frac{\log\zeta(s)}{\zeta(s)-1}-1.\end{equation}
Defining $S(X)=\sum_{n\le X} b(n)$ by $\Phi(s)=\sum_{n\ge1} b(n)n^{-s}$ and $A(X)=X-S(X)$, my goal is to prove eventual positivity of...