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#1 2010-06-14 06:39:13

kat-m
Member
Registered: 2010-06-14
Posts: 2

help me on the set notation

Let

and
. Let
for
and
. Then, show

i dont get this at  all. please help me

Last edited by kat-m (2010-06-14 06:40:52)

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#2 2010-06-14 11:55:47

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: help me on the set notation

i dont get this at  all.

Good.  Because you shouldn't.  delta is a subset of R^2, and I_n is a subset of R.  The statement "d = \cap I_n" doesn't make sense.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2010-06-14 23:54:02

kat-m
Member
Registered: 2010-06-14
Posts: 2

Re: help me on the set notation

Thats what i thought. so how do you show

is measurable if you suppose
and
are complete measure spaces, where
is legesgue measure and
is counting measure?

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#4 2010-06-15 10:16:00

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: help me on the set notation

Think about dividing the square [0,1] x [0,1] into n^2 little blocks.  Then you want to only include those little blocks which contain some piece of delta.  Which are those going to be?  Now do this as n goes to infinity by taking an intersection.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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