On Thu, 6 Jun 2013 15:00:04 -0700 (PDT), email@example.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 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?