Theorems · Theorem · complex analysis
intervalIntegrable_log_sin
∀ {a b : ℝ}, IntervalIntegrable (Real.log ∘ Real.sin) MeasureTheory.volume a bSpecial case of MeromorphicOn.intervalIntegrable_log: The function log ∘ sin is interval
integrable over every interval.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Real.logstatement · cited by 939
- Real.sinstatement · cited by 389
- IntervalIntegrablestatement · cited by 316
- AnalyticOnNhd.meromorphicOnproof · cited by 13
- MeromorphicOn.intervalIntegrable_logproof · cited by 2
- Real.analyticOnNhd_sinproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- integral_log_sin_zero_pi_div_twoproof · cited by 1