In mathematics, specifically in class theories, the axiom of global choice is a stronger variant of the axiom of choice that applies to proper classes of sets as well as sets of sets. Informally it states that one can simultaneously choose an element from every non-empty set.
== Statement ==
The axiom of global choice states that there is a global choice function τ, meaning a function such that for every non-empty set z, τ(z) is an element of z.
The axiom of global choice cannot be stated directly in the language of ZFC (Zermelo–Fraenkel set theory with the axiom of choice), as the choice function...
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Consider Tommy’s integrals:
$$a) \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^4}\, dx = \frac{5 }{36}\pi ^2 $$
$$ b) \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^5}\, dx = \frac{5}{72} \pi^2 - \frac{ ln^{2}(3) }{4} - \frac{ \text{Li}_2(1/3) }{2} $$
$$ c) \int_0^1 \fr...
In mathematics, the restricted product is a construction in the theory of topological groups.
Let
I
{\displaystyle I}
be an indexing set;
S
{\displaystyle S}
a finite subset of
I
{\displaystyle I}
. If for each
i
∈
I
{\displaystyle i\in I}
,
G
i
{\displaystyle G_{i}}
is a locally compact group, and for each
...
