Proof about metric spaces

Proof about metric spaces

Postby Guest » Tue Jan 12, 2021 5:08 am

Hi everyone,
I have been recently working on metric spaces, doing some exercises about proving properties, integrability... But there's one I have not idea how to prove it (or maybe I should give an counterexample).
I have to prove if there exists a metric space (X,M,[tex]\mu[/tex]) such that {[tex]\mu[/tex](E) : such that E [tex]\in[/tex] M} = [0,+[tex]\infty[/tex]]\Q[tex]^{+}[/tex]

If anyone has an idea I would be delighted to read u, thanks in advan
Guest
 

Re: Proof about metric spaces

Postby HallsofIvy » Fri Jan 15, 2021 11:00 am

It looks like you are simply asking if it is possible to give a metric to the set of all positive irrational numbers. Is that correct?

HallsofIvy
 
Posts: 318
Joined: Sat Mar 02, 2019 9:45 am
Reputation: 108

Re: Proof about metric spaces

Postby HallsofIvy » Fri Jan 15, 2021 6:57 pm

You can always give the "discrete metric" to any set with d(x, x)= 1, d(x, y)= 0.

HallsofIvy
 
Posts: 318
Joined: Sat Mar 02, 2019 9:45 am
Reputation: 108


Return to Calculus - integrals, lim, functions



Who is online

Users browsing this forum: No registered users and 1 guest