Theorems · Theorem · measure theory
MeasureTheory.integral_mconv
∀ {M : Type u_1} {F : Type u_2} [inst : Monoid M] {mM : MeasurableSpace M} [MeasurableMul₂ M]
[inst_2 : NormedAddCommGroup F] {μ ν : MeasureTheory.Measure M} {f : M → F} [inst_3 : NormedSpace ℝ F]
[MeasureTheory.SFinite μ] [MeasureTheory.SFinite ν],
MeasureTheory.Integrable f (μ.mconv ν) → ∫ (x : M), f x ∂μ.mconv ν = ∫ (x : M), ∫ (y : M), f (x * y) ∂ν ∂μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 265 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Monoidstatement and proof · cited by 3,887
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasurableMul₂statement and proof · cited by 139
- MeasureTheory.integral_mapproof · cited by 67
- aemeasurable_idproof · cited by 66
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