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




Re: Proof of easy case of change of variables
Posted:
Jun 7, 2013 12:10 PM


On Thu, 6 Jun 2013 15:00:04 0700 (PDT), pepstein5@gmail.com 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 n1 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 nonstandard). > >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 onevariable integral? Ie for n = 2, int f = int(int f(x,y) dx)dy?
> >Thank You, > >Paul Epstein



