Lengths are closed intervals. The idea of length {theory of content} {content theory} can extend to open intervals. For open intervals, sum of subintervals that enclose points has greatest lower bound {outer content} and sum of polygonal regions makes least upper bound {inner content}. If outer content is less than or equal to inner content, interval has content.
length
If inner content equals outer content, inner content is interval length for one dimension.
additive
For finite number of intervals, sum of disjoint sets with content is sum of set contents {additivity property}.
Mathematical Sciences>Calculus>Analysis>Theorem
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Date Modified: 2022.0224