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Analysis III

Post Icon Posted: Submitted by Sammy P 06 on 27 October 2007 - 4:13pm.

Joined: 2006-11-04
Posts: 53

I just have a question regarding clarification of notation, any help is appreciated! On Assignment 3 Question 10 reads: ``If $ f $ is regulated and is the uniform limit of weakly increasing step functions show that $ f $ is weakly increasing.''

Is the statement `$ f $... is the uniform limit of weakly increasing step functions' equivalent to `$ \exists $ a sequence of weakly increasing step functions $ (\phi_n) $ such that $ \lim_{n\rightarrow\infty}\|f-\phi_n\|_\infty = 0 $'?

Thanks!

P.S. keyboards with misplaced `\' keys are diabolical for $ \LaTeX $!

‹ Dg Errata Product rule of convergence sequence proof ›
Post Icon Posted: 27 October 2007 - 7:30pm

Joined: 2006-11-02
Posts: 1004

Yep.

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