Editing Chebotarev density theorem (section)

===Infinite extensions===
The statement of the Chebotarev density theorem can be generalized to the case of an infinite Galois extension ''L'' / ''K'' that is unramified outside a finite set ''S'' of primes of ''K'' (i.e. if there is a finite set ''S'' of primes of ''K'' such that any prime of ''K'' not in ''S'' is unramified in the extension ''L'' / ''K''). In this case, the Galois group ''G'' of ''L'' / ''K'' is a [[profinite group]] equipped with the Krull topology. Since ''G'' is compact in this topology, there is a unique [[Haar measure]] μ on ''G''. For every prime ''v'' of ''K'' not in ''S'' there is an associated Frobenius conjugacy class ''F''<sub>v</sub>. The Chebotarev density theorem in this situation can be stated as follows:<ref name="Section" />

:Let ''X'' be a subset of ''G'' that is stable under conjugation and whose boundary has Haar measure zero. Then, the set of primes ''v'' of ''K'' not in ''S'' such that ''F''<sub>v</sub> ⊆ X has density
::<math>\frac{\mu(X)}{\mu(G)}.</math>

This reduces to the finite case when ''L'' / ''K'' is finite (the Haar measure is then just the counting measure).

A consequence of this version of the theorem is that the Frobenius elements of the unramified primes of ''L'' are dense in ''G''.