I think the textbook wants to talk about a generating set (base) for the $\sigma$-algebra $\mathcal{A}$ and so in particular $\mathcal{G} \subseteq \mathcal{A} \subseteq \mathscr{P}(X)$. That's about all we know.
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e. the nodes are located in a space equipped with a certain metric. The simplest mathematical realization is a lattice or a random geometric graph, where nodes are distributed uniformly at random over a two-dimensional plane; a pair of nodes are connected if the Euclidean distance is smaller than a given neighborhood radius. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks and neural...
Is anything known about this sum? I'm summing over the primes, $p.$
$$ \sum_p \frac{1}{2^p} $$
I've calculated that it converges, but I can't determine whether the following related sum can be analytically continued outside the unit circle:
$$\sum_p z^{-p}$$
In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. It states that
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Having had my formative years in New Zealand, I was born in South Africa. I vaguely recall when I was VERY young having someone tell me when I said "hey" that "hay is what horses eat".
I got that then it was more when people would yell "hey" across a room to attract attention, and that was co...
This is related to a remark in Iitaka's algebraic geometry sec 1.12.
"...It should be noted that sheaves of germs of differentiable functions are by no means coherent. These facts seem to suggest coherence is linked with the property of being algebraic or analytic."
$\textbf{Q1:}$ What is the ...
