Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_one
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s : Set α), ∫⁻ (x : α) in s, 1 ∂μ = μ s- Cited by
- 17 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- one_mulproof · cited by 2,841
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.setLIntegral_constproof · cited by 11
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.IsAddFundamentalDomain.measure_eq_tsumproof · cited by 5
- MeasureTheory.IsFundamentalDomain.measure_eq_tsumproof · cited by 4
- MeasureTheory.measure_add_lintegral_eqproof · cited by 3
- MeasureTheory.measure_mul_lintegral_eqproof · cited by 3
- MeasureTheory.Measure.rnDeriv_le_one_of_leproof · cited by 2
- MeasureTheory.IsFundamentalDomain.measure_eqproof · cited by 1
- MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_acproof · cited by 1
- MeasureTheory.measure_add_measure_eqproof · cited by 1
- MeasureTheory.ae_measure_preimage_add_right_lt_topproof · cited by 1
- MeasureTheory.ae_measure_preimage_mul_right_lt_topproof · cited by 1
- MeasureTheory.measure_mul_measure_eqproof · cited by 1
- MeasureTheory.IsAddFundamentalDomain.measure_eqproof · cited by 1