Talk:Almost periodic function

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[edit] Quasiperiodic function vs Almost periodic function

Is the link to Quasiperiodic function really necessary? I thought that one was the same as "almost periodic", and I would suggest the redirect from Quasiperiodic function be made to point here, rather than to Quasiperiodic tiling. Suggestions? Oleg Alexandrov 16:15, 13 Feb 2005 (UTC)

PS. I ran into this when considering copying the PlanetMath article quasiperiodic function. Oleg Alexandrov 16:15, 13 Feb 2005 (UTC)

No, they are very different. At least, 'quasiperiodic' has at least two meanings. Charles Matthews 16:36, 13 Feb 2005 (UTC)

Got it. One day it might be nice to actually have an article on that. Oleg Alexandrov 17:08, 13 Feb 2005 (UTC)

[edit] The set of epsilon-periods must be "evenly space" or "relatively dense"

The assertion "He proved that this definition was equivalent to the existence of ε almost-periods, for all ε > 0: that is, translations T(ε) = T of the variable t making |f(t+T)-f(t)|<ε" is wrong.

The correct form is to say that given any positive ε, there exists a positive L(ε) such that for any real x, the interval [x, x+L(ε)] contains an ε almost-period, that is, a τ such that |f(t+τ)-f(t)|<ε, for all real t.

Note that if T makes |f(t+T)-f(t)|<ε it is not necessary that |f(t+2*T)-f(t)|<ε, that is, that k*T, k integer, form a set of ε almost-periods, hence the necessity of the L(ε). User:jcpspbr 2006-08-29