fix: restore determinant scaling factor to measure_linear - #636
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fix: restore determinant scaling factor to measure_linear#636Chessing234 wants to merge 1 commit into
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Exercise 1.1.11(2) states the linear image measure scales by D (the witness the statement itself introduces), matching measure_linear_of_elem and measure_linear_det right below it, plus the doc comment. As written the RHS dropped D entirely, i.e. claimed linear maps preserve Jordan measure exactly, which is false (e.g. x -> 2x doubles the measure of [0,1]).
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exercise 1.1.11(2):
measure_linear's conclusion dropped theDit existentially introduces, so as stated it claims linear maps preserve jordan measure exactly. counterexample:x ↦ 2xon[0,1]doubles the measure. the elementary-set version right above (measure_linear_of_elem) andmeasure_linear_detright below both already assume/use theD *factor, and the doc comment says "up to determinant scaling" - so this just brings the statement in line with its neighbors.