fix: three false statements (Egorov domain, 10.4.1/9.3.21 Nat div, Lusin caution)#601
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fix: three false statements (Egorov domain, 10.4.1/9.3.21 Nat div, Lusin caution)#601Chessing234 wants to merge 7 commits into
Chessing234 wants to merge 7 commits into
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With n : ℕ, (1/n:ℝ) is Nat.div (0 for n ≥ 2), so x^(1/n) collapses to the constant 1 and the stated derivative is false. Co-authored-by: Cursor <cursoragent@cursor.com>
The finite-measure refinement should converge on S outside the small exceptional set, not on the complement Sᶜ ∪ E. Co-authored-by: Cursor <cursoragent@cursor.com>
(1/n:ℝ) for n : ℕ is Nat.div, so the sequence is eventually f(0) instead of f(1/n) along positive rationals. Co-authored-by: Cursor <cursoragent@cursor.com>
ContinuousOn (1_ℚ) (ℝ \ ℚ) holds, so the old claim is false; the intended caution is that ambient ContinuousAt can fail on Eᶜ. Co-authored-by: Cursor <cursoragent@cursor.com>
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Summary
S ∩ Eᶜ, notSᶜ ∪ E.1/(n:ℝ)so the exponent/argument is real division, notNat.div.ContinuousAtonEᶜ(ContinuousOnholds for1_ℚ).Feature branches merged here:
fix/egorov-finite-measure-domain,fix/nat-div-real-exponents,fix/lusin-caution-continuous-at.Test plan
lake build Analysis.MeasureTheory.Section_1_3_5 Analysis.Section_10_4 Analysis.Section_9_3