Majorization of summable sequences
= Majorization of summable sequences
{title2=$x\prec y$}
For decreasing positive sequences in $\ell^1$, write $x\prec y$ if every initial <partial sum> of $x$ is at most the corresponding <partial sum> of $y$ and the finite total sums agree. The finiteness requirement matters: equality of two divergent totals interpreted as infinity is too weak to guarantee a <doubly stochastic realization of summable-sequence majorization>.