3 The electrostatic potential generated by a distribution of electric charge in R with density p: R³ → R is defined to by p(x - y)®y. Р(х — у) d³y. 47|y| 6(x) Show that this integral is absolutely...

The electrostatic potential generated by a distribution of electric charge in R with density p: R³ → R is defined to by p(x - y)y. Р(х — у) d³y. 47|y| 6(x) Show that this integral is absolutely convergent if p is continuous and vanishes outside a bounded set (that is, there is some bounded set S for which p(x) = 0 for all x ¢ S).

Extracted text: 3 The electrostatic potential generated by a distribution of electric charge in R with density p: R³ → R is defined to by p(x - y)®y. Р(х — у) d³y. 47|y| 6(x) Show that this integral is absolutely convergent if p is continuous and vanishes outside a bounded set (that is, there is some bounded set S for which p(x) = 0 for all x ¢ S).