Theorems · Theorem · measure theory
isPiSystem_prod
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β],
IsPiSystem (Set.image2 (fun x1 x2 => x1 ×ˢ x2) {s | MeasurableSet s} {t | MeasurableSet t})Rectangles form a π-system.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.ofPredstatement · cited by 6,101
- MeasurableSetstatement · cited by 3,075
- SProd.sprodstatement · cited by 1,750
- Set.image2statement · cited by 311
- IsPiSystemstatement · cited by 88
- MeasurableSpace.isPiSystem_measurableSetproof · cited by 14
- IsPiSystem.prodproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.measurable_kernel_prodMk_left_of_finiteproof · cited by 1
- measurable_measure_prodMk_left_finiteproof · cited by 1
- MeasureTheory.ae_eq_of_setLIntegral_prod_eqproof · cited by 1
- MeasureTheory.VectorMeasure.prod_eq_of_forall_apply_prodproof · cited by 1
- MeasureTheory.Measure.prodAssoc_prodproof · cited by 1
- ProbabilityTheory.lintegral_toKernel_memproof · cited by 1
- MeasureTheory.Measure.ext_prodproof · cited by 1
- MeasureTheory.Measure.ext_prod₃proof · cited by 1
- MeasureTheory.VectorMeasure.stronglyMeasurable_vectorMeasure_prodMk_leftproof · cited by 1
- MeasureTheory.ProbabilityMeasure.measurable_fun_prodproof · cited by 0
- MeasureTheory.FiniteMeasure.measurable_fun_prodproof · cited by 0