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Topic: Proof of easy case of change of variables
Replies: 5   Last Post: Jun 8, 2013 5:31 PM

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David C. Ullrich

Posts: 3,555
Registered: 12/13/04
Re: Proof of easy case of change of variables
Posted: Jun 7, 2013 12:10 PM
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On Thu, 6 Jun 2013 15:00:04 -0700 (PDT), wrote:

>In Principles of Mathematical Analysis, Rudin defines a function f from R^n to R^n as being "primitive" if, for all x, at least n-1 of the coordinates of
>(x - f(x)) are equal to 0.

Not quite - the quantifiers are in a different order. You realy might
give page numbers, btw.

> (I didn't encounter anyone else using this definition when I did a google search so I'm guessing (with barely more than 50% confidence) that this usage is non-standard).
>I'm trying to follow Rudin's proof of the change of variable formula for integration in the context of multivariable calculus.
>He proves it for the case n = 1 and then asserts that it is clear for primitive functions. However, it's not clear to me. Can anyone give any pointers about how to
>progress from the n = 1 case to the case of more general primitive functions?

Has he proved a "Fubini" sort of theorem yet, to the effect that the
integral of a function of several variables is equal to an iterated
one-variable integral? Ie for n = 2, int f = int(int f(x,y) dx)dy?

>Thank You,
>Paul Epstein

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