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Forum index » Science and Technology » Math
norms
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vsgdp
science forum addict


Joined: 01 May 2005
Posts: 78

PostPosted: Wed May 04, 2005 2:54 am    Post subject: norms Reply with quote
Hi,

I need to show ||f|| = integral( abs(f) dx, a, b) is a norm on the set of
continuous functions on [a, b].

I know I need to show the 4 properties, but in particular, I am having
trouble showing triangle inequality. Basically, the absolute value is
giving me problems. Any hints?
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A. Boom
science forum addict


Joined: 28 Apr 2005
Posts: 65

PostPosted: Wed May 04, 2005 3:32 am    Post subject: Re: norms Reply with quote
vsgdp wrote:
Quote:
Hi,

I need to show ||f|| = integral( abs(f) dx, a, b) is a norm on the set of
continuous functions on [a, b].

I know I need to show the 4 properties, but in particular, I am having
trouble showing triangle inequality. Basically, the absolute value is
giving me problems. Any hints?



I've never done what you are attempting, but might you show the
inequality hold for integral( f dx, a, b) and also integral (-f dx, a,
b), and if it holds for both then it holds for integral (abs(f) dx, a, b).

Adam.
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Proginoskes
science forum Guru


Joined: 29 Apr 2005
Posts: 2593

PostPosted: Wed May 04, 2005 4:13 am    Post subject: Re: norms Reply with quote
vsgdp wrote:
Quote:
Hi,

I need to show ||f|| = integral( abs(f) dx, a, b) is a norm on
the set of continuous functions on [a, b].

I know I need to show the 4 properties, but in particular, I
am having trouble showing triangle inequality. Basically, the
absolute value is giving me problems. Any hints?

Use the property of integrals that says if F(x) <= G(x) for all x
in the interval, then
integral (F(x) dx, a, b) <= integral( G(x) dx, a, b),
along with the triangle inequality for real numbers.

This should be more than enough of a hint.
--- Christopher Heckman
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Google
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