Theorems · Theorem · measure theory
MeasureTheory.Integrable.swap
∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
{μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
[MeasureTheory.SFinite μ] ⦃f : α × β → E⦄,
MeasureTheory.Integrable f (μ.prod ν) → MeasureTheory.Integrable (f ∘ Prod.swap) (ν.prod μ)- Defined in
- Mathlib.MeasureTheory.Integral.Prod
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.prodstatement and proof · cited by 353
- MeasureTheory.integrable_swap_iffproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.prod_right_aeproof · cited by 4
- MeasureTheory.integral_prod_symmproof · cited by 2
- MeasureTheory.Integrable.of_comp_fstproof · cited by 1
- MeasureTheory.Integrable.integral_prod_rightproof · cited by 1
- MeasureTheory.Integrable.integral_norm_prod_rightproof · cited by 0
- MeasureTheory.IntegrableOn.swapproof · cited by 0
- MeasureTheory.integral_integral_symmproof · cited by 0