Theorems · Theorem · measure theory
MeasureTheory.lintegral_zero
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}, ∫⁻ (x : α), 0 ∂μ = 0- Cited by
- 18 results in Mathlib
- Foundations
- Depth 196 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.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.univproof · cited by 3,945
- MulZeroClass.zero_mulproof · cited by 1,625
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.lintegral_constproof · cited by 123
Cited by18
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_measurable_le_lintegral_eqproof · cited by 8
- MeasureTheory.quasiMeasurePreserving_invproof · cited by 7
- MeasureTheory.quasiMeasurePreserving_negproof · cited by 7
- MeasureTheory.mul_meas_ge_le_lintegral₀proof · cited by 5
- MeasureTheory.Measure.lintegral_rnDeriv_lt_top_of_measure_ne_topproof · cited by 2
- ProbabilityTheory.lintegral_gammaPDF_eq_oneproof · cited by 2
- MeasureTheory.tendsto_lintegral_norm_of_dominated_convergenceproof · cited by 2
- MeasureTheory.absolutelyContinuous_of_isAddLeftInvariantproof · cited by 1
- MeasureTheory.absolutelyContinuous_of_isMulLeftInvariantproof · cited by 1
- MeasureTheory.lintegral_eq_zero_of_ae_eq_zeroproof · cited by 1
- MeasureTheory.QuasiMeasurePreserving.prod_of_rightproof · cited by 1
- ProbabilityTheory.lintegral_exponentialPDF_eq_antiDerivproof · cited by 1