fix: Exercise 1.1.7(i) needs a closed box - #648
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A Box is a product of BoundedIntervals, which need not be closed, and ContinuousOn f B.toSet on a non-closed box does not force f to be bounded. Taking d = 1, B = Ioo 0 1 and f x = 1 / x (continuous on B.toSet) makes the graph, and the region under it, unbounded, so neither is Jordan measurable -- JordanMeasurable carries a boundedness field. Requiring IsClosed B.toSet makes B.toSet compact, so f is bounded and uniformly continuous there, which is the hypothesis the textbook exercise uses. IsClosed B.toSet is the same way closed boxes are spelled elsewhere (Section_1_2_1). Signed-off-by: Taksh <takshkothari09@gmail.com>
This was referenced Aug 15, 2026
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A
Box dis a product ofBoundedIntervals, which need not be closed, andContinuousOn f B.toSetover a non-closed box does not forcefto be bounded.Counterexample to the statement as formalized: take
d = 1,B.side 0 = Ioo 0 1, andf x = 1 / x 0(away from 0, soContinuousOn f B.toSetholds). Thenis unbounded in its second coordinate, and so is the region under it.
JordanMeasurablecarries a boundedness field, so neither set is Jordan measurable and bothgraphandundergraphare false.Adding
(hB : IsClosed B.toSet)makesB.toSetcompact, so a continuousfis bounded and uniformly continuous there — the closed-box hypothesis the textbook exercise uses.IsClosed B.toSetis how closed boxes are already spelled inSection_1_2_1.lean.measure_of_graphpicks up the hypothesis too since it refers toJordanMeasurable.graph. All three bodies staysorry, and none of the three lemmas is referenced elsewhere in the repository.