Theorems · Theorem · measure theory
MeasureTheory.measure_smul_setAverage
∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
{μ : MeasureTheory.Measure α} (f : α → E) {s : Set α},
μ s ≠ ⊤ → μ.real s • ⨍ (x : α) in s, f x ∂μ = ∫ (x : α) in s, f x ∂μ- Defined in
- Mathlib.MeasureTheory.Integral.Average
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Factproof · cited by 2,726
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
Cited by1
Results whose statement or proof uses this declaration.
- ae_eq_const_or_exists_average_ne_complproof · cited by 2