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Specifically I was looking at this example given here: http://mathworld.wolfram.com/ConvolutionTheorem.html

But is it true that for any equation, you are allowed to change the order of integration without doing anything if the limits are from negative infinity to infinity?

$\int_{-\infty}^\infty F(t) \int_{-\infty}^\infty G(v) dvdt = \int_{-\infty}^\infty G(v) \int_{-\infty}^\infty F(t) dtdv$?

What if the inner function is a function of both variables: G(t,v), where G(t,v) is a function in the inner integral.

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    I'm kind of confused about this. I forgot all the rules about the change in order of integration – 2017-02-01
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    The function that's only in the outer integral can't depend on the variable of the inner integral, because it's not defined outside of the inner integral. – 2017-02-01
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    @xavierm02 Oh, yeah you're right. How about both variables in just the inner integral? – 2017-02-01
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    Writing the left term of your equality implies that $F$ only has one argument, and the same things happens for $G$ with the right term. So either side could make sense with one function depending on two variables (and the other depending on one variable) but if you want both sides to make sense, both functions can only depend on one variable. – 2017-02-01
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    Take a look at [Fubini's theorem](https://en.wikipedia.org/wiki/Fubini's_theorem). In general, you need [uniform convergence](https://en.wikipedia.org/wiki/Uniform_convergence). – 2017-02-01

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