(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that inR[itex]^{n}[/itex], the euclidean metric, the d[itex]_{\infty}[/itex]=max{|a1-b1|,...,|a[itex]_{n}[/itex]}-b[itex]_{n}[/itex]|}, and d = |a1-b1|+...|a[itex]_{n}[/itex]}-b[itex]_{n}[/itex]|.

2. Relevant equations

Uniform Equivalence: basically p,d so that we have the two inequalities with some constants like p(x,y)[itex]\leq[/itex]Ad(x,y) and d(x.y)[itex]\leq[/itex]Bp(x,y).

Schwarz inequality.

3. The attempt at a solution

I was going to do this in straightforward manner but when we go to see what our constants are, they turn out to n or [itex]\infty[/itex]. I don't know what to do. Can we treat them as coefficients in the two respective ineqaulities?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Uniformly Equivalent Metrics

**Physics Forums | Science Articles, Homework Help, Discussion**