Geodesic
Some results on the product of distributions and the change of variable
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 677-685.

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Let $F$ and $G$ be distributions in $\Cal D'$ and let $f$ be an infinitely differentiable function with $f'(x)>0$, (or $0$). It is proved that if the neutrix product $F\circ G$ exists and equals $H$, then the neutrix product $F(f)\circ G(f)$ exists and equals $H(f)$.
Classification : 46F10
Keywords: distribution; neutrix product; change of variable 
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Özçag, Emin; Fisher, Brian. Some results on the product of distributions and the change of variable. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 677-685. http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a9/