Theorems · Theorem · number theory
UpperHalfPlane.volume_eq_lintegral
∀ (s : Set UpperHalfPlane), MeasureTheory.volume s = ∫⁻ (z : ℂ) in UpperHalfPlane.coe '' s, ↑((1 / ‖z.im‖₊) ^ 2)
Express the volume of a measurable set as a Lebesgue integral
over the corresponding subset of ℂ.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement · cited by 25,697
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- ENNRealstatement and proof · cited by 9,879
- Set.imagestatement and proof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Set.rangeproof · cited by 4,705
- NNRealstatement · cited by 4,310
- LT.lt.leproof · cited by 2,189
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
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