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$$\frac{1}{\mu(B)}\int_B \vert x \vert d\mu(x) = \frac{1}{p+1}$$
This formula holds for the unit ball in $\mathbb{Q_p}$. This formula also holds for $\mathbb{R}$ when $p=1$. Should one expect $$W_{1^{\infty}} \mathrm{Frac}(W_{1^{\infty}} (\mathbb{F_1})=\mathbb{R}?$$ \mathbb{F_1}))=\mathbb{R}?$$What (mathematical) criteria do people use to rule-out field with one element phenomena? What makes point counting formulas better (or worse)? 2 edited body$$\frac{1}{\mu(B)}\int_B \vert f x \vert d\mu(x) = \frac{1}{p+1}$$This formula holds for the unit ball in \mathbb{Q_p}. This formula also holds for \mathbb{R} when p=1. Should one expect$$W_{1^{\infty}} (\mathbb{F_1})=\mathbb{R}? What (mathematical) criteria do people use to rule-out field with one element phenomena? What makes point counting formulas better (or worse)?