= Double series
{title2=$\sum_m\sum_n a_{mn}$}
A <double series> is a <series> whose terms carry two indices. For nonnegative terms, define its sum as the supremum of all finite subsums; iterated sums in either order give this same value, possibly infinity. For absolutely summable terms, both orders also agree and give a finite sum. Without these hypotheses, an order of summation must be specified and changing it can change the result. A triangular index set, such as $0\le n\le m$, can be represented by setting the other terms to zero.
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