Theorems · Theorem · measure theory
MeasureTheory.lintegral_const
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (c : ENNReal), ∫⁻ (x : α), c ∂μ = c * μ Set.univ- Cited by
- 123 results in Mathlib
- Foundations
- Depth 195 from the axioms, rests on 4,709 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · 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
- Set.univstatement · cited by 3,945
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.SimpleFunc.constproof · cited by 50
- MeasureTheory.SimpleFunc.lintegral_eq_lintegralproof · cited by 15
- MeasureTheory.SimpleFunc.const_lintegralproof · cited by 2
- MeasureTheory.SimpleFunc.coe_constproof · cited by 1
Cited by123
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_dirac'proof · cited by 19
- MeasureTheory.lintegral_zeroproof · cited by 18
- MeasureTheory.lintegral_const_mul'proof · cited by 15
- MeasureTheory.lintegral_oneproof · cited by 14
- MeasureTheory.lintegral_diracproof · cited by 13
- MeasureTheory.lintegral_indicator_oneproof · cited by 13
- MeasureTheory.setLIntegral_constproof · cited by 11
- MeasureTheory.withDensity_oneproof · cited by 8
- MeasureTheory.eLpNorm'_zeroproof · cited by 5
- MeasureTheory.lintegral_withDensity_eq_lintegral_mulproof · cited by 5
- MeasureTheory.withDensity_constproof · cited by 4
- ProbabilityTheory.Kernel.swap_parallelCompproof · cited by 4