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distance between sets
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Dave L. Renfro
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Joined: 29 Apr 2005
Posts: 570

PostPosted: Thu Jul 13, 2006 6:53 pm    Post subject: Re: distance between sets Reply with quote

diegotorquemada@yahoo.com wrote:

Quote:
Suppose X and Y are two closed, bounded and convex sets.

I need a metric such that d(X,Y) = 0 iff X=Y.

for example the Hausdorff metric
(http://planetmath.org/encyclopedia/HausdorffMetric.html)
can help me.

Is there any other "popular" metric that has that property?

?? *Every* metric satisfies d(X,Y) = 0 iff X=Y.
(Well, maybe not in general relativity ...)

Nevertheless, perhaps some of the following could be useful:

http://www.fas.org/sgp/othergov/doe/lanl/pubs/00285752.pdf

http://tinyurl.com/hdqzf

http://www.maths.warwick.ac.uk/~jcr/re/usc.pdf [see p. 3]

http://www.sztaki.hu/~szatmari/thesis.pdf

http://cadpipe.vtt.fi/documents/hardwbasrenddataredu.pdf [pp. 36-38?]

Dave L. Renfro
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step_y@yahoo.com
science forum beginner


Joined: 13 Jul 2006
Posts: 1

PostPosted: Thu Jul 13, 2006 6:16 pm    Post subject: Re: distance between sets Reply with quote

sure sounds pretty interesting







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diegotorquemada@yahoo.com wrote:
Quote:
Hello

Suppose X and Y are two closed, bounded and convex sets.

I need a metric such that d(X,Y) = 0 iff X=Y.

for example the Hausdorff metric
(http://planetmath.org/encyclopedia/HausdorffMetric.html) can help
me.

Is there any other "popular" metric that has that property?

thanks a lot for your answer

Diego
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diegotorquemada@yahoo.com
science forum beginner


Joined: 11 Oct 2005
Posts: 17

PostPosted: Thu Jul 13, 2006 4:47 pm    Post subject: distance between sets Reply with quote

Hello

Suppose X and Y are two closed, bounded and convex sets.

I need a metric such that d(X,Y) = 0 iff X=Y.

for example the Hausdorff metric
(http://planetmath.org/encyclopedia/HausdorffMetric.html) can help
me.

Is there any other "popular" metric that has that property?

thanks a lot for your answer

Diego
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