/sci/ - Science & Math

Requesting a slick, satisfying proof of this.
Example of non-slick, dissatisfying proof:
[math]\text{There is an } x' \text{ and a } y' \text{ such that } x' \neq y' \text{ and } K(x', y') \neq 0. \\ \text{Then we can take a bump function } f \text{ centered on } y' \text{ such that } f(x') = 0. \\ \text{If necessary, we can pass to } g(x) = f(y' + \epsilon (x - y')) \text{ for large epsilon to guarantee that the integral doesn't zero, q.e.d.}[/math]