Theorems · Theorem · measure theory
MeasureTheory.Measure.measurePreserving_swap
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
{ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ],
MeasureTheory.MeasurePreserving Prod.swap (μ.prod ν) (ν.prod μ)- Defined in
- Mathlib.MeasureTheory.Measure.Prod
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 223 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.prodstatement · cited by 353
- MeasureTheory.MeasurePreservingstatement · cited by 259
- measurable_swapproof · cited by 42
- MeasureTheory.Measure.prod_swapproof · cited by 14
Cited by16
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_prod_swapproof · cited by 3
- MeasureTheory.integrable_swap_iffproof · cited by 3
- MeasureTheory.NullMeasurableSet.left_of_prodproof · cited by 2
- MeasureTheory.measurePreserving_prod_add_swapproof · cited by 2
- MeasureTheory.measurePreserving_prod_add_swap_rightproof · cited by 2
- MeasureTheory.measurePreserving_prod_div_swapproof · cited by 2
- MeasureTheory.measurePreserving_prod_inv_mul_swapproof · cited by 2
- MeasureTheory.measurePreserving_prod_mul_swapproof · cited by 2
- MeasureTheory.measurePreserving_prod_mul_swap_rightproof · cited by 2
- MeasureTheory.measurePreserving_prod_neg_add_swapproof · cited by 2
- MeasureTheory.lintegral_prod_swapproof · cited by 2
- MeasureTheory.measurePreserving_prod_sub_swapproof · cited by 2