- #1

CantorSet

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This question is a bit involved but it pertains to calculating the differential of a variable substitution used in the proof of the convolution theorem (http://en.wikipedia.org/wiki/Convolution_theorem)

Consider

[tex] \int f(t) \int g(s - t) ds dt.[/tex]

If we use the substitution

[tex]r = s - t [/tex]

we get the differential relation as

[tex]dr = ds[/tex]

so the above equation becomes

[tex] = \int f(t) \int g(r) dr dt = \int f(t) dt \int g(r) dr [/tex]

But why didn't we use the differential relation

[tex]dr = ds - dt[/tex] ?