For historical reasons, the term " Jordan measure " is now well-established, despite the fact that it is not a true measure in its modern definition, since Jordan-measurable sets do not form a ?-algebra.
12.
One cannot define the Jordan measure of " S " as simply the sum of the measures of the individual rectangles, because such a representation of " S " is far from unique, and there could be significant overlaps between the rectangles.
13.
Sen . Phil Gramm, R-Texas, said the Jordan measure was a threat to U . S . sovereignty because, he said, an international tribunal could rule that labor or environmental laws written by Congress were detrimental to trade, making the United States liable for sanctions.
14.
Luckily, any such simple set " S " can be rewritten as a union of another finite family of rectangles, rectangles which this time are mutually disjoint, and then one defines the Jordan measure " m " ( " S " ) as the sum of measures of the disjoint rectangles.
