The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: subseries of harmonic series converges iff ...
Replies: 5   Last Post: Nov 21, 2004 9:11 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Michael Hamm

Posts: 84
Registered: 12/6/04
Re: subseries of harmonic series converges iff ...
Posted: Nov 21, 2004 9:11 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Yesterday, The World Wide Wade <> wrote,
in part:
> > >I recall reading a theorem once that says
> > > For a subset S of Z+ , the following are equivalent:
> > > * \Sum_{s \in S} 1/s < \infty
> > > * Something else.
> > >
> > >Does anyone know what that something else is?
> >
> > I was hoping someone else would give the correct answer but I was
> > under the impression there's a correct "Something else" of the form,
> > * { x^s, s \in S } is a basis for C[0,1]
> > (the set of continuous functions on the interval). Or something like that.

> This is the Muntz-Szasz theorem: If 0 < p1 < p2 < p3 < ..., then the span
> of {1, x^p1, x^p2, ...} is dense in C[0,1] iff 1/p1 + 1/p2 + ... = oo.
> (There is a nice proof of this in Rudin's Real and Complex Analysis.)

Thank you both!

Michael Hamm
AM, Math, Wash. U. St. Louis Standard disclaimers:
<a href=""></a> ... legal.html

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.