Is the rearrangement inequality generalizable for infinite number of variables?
In other words if I have an infinite sum
$a_1x_1 + a_2x_2 + ... $
And we can change the order of the coefficients. If we know that $x_1 \geq x_2 \geq \dots$ is it always optimal to choose $a_1 \geq a_2 \geq \dots$ if we want to maximize the sum?