2

I am not too familiar with Fourier analysis, but I needed to use a certain result. I would appreciate any assistance.

I was reading a literature in Foruier analysis and it said something like "Every infinite discrete abelian group $G$ contains a set $E$ which satisfies (Property A)."

I was wondering if someone could tell me what do they mean by discrete group here. I looked up Wikipedia and it said that it is a group with discrete topology and that every group can be given a discrete topology.

So is that mean that the $G$ above can actually be any infinite abelian group? Thanks!

Tom Mosher
  • 1,349
  • 8
  • 12

1 Answers1

0

Yes, a discrete group is an arbitrary group equipped with the discrete topology. This is often done when another group with a nontrivial topology is likely to show up, as will certainly happen in Fourier analysis, essentially because the Pontryagin dual of a discrete group is in general not discrete.

Kevin Carlson
  • 52,457
  • 4
  • 59
  • 113