Theorems · Theorem · measure theory

MeasureTheory.Measure.pi_eval_preimage_null

∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
  (μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)] {i : ι} {s : Set (α i)},
  (μ i) s = 0 → (MeasureTheory.Measure.pi μ) (Function.eval i ⁻¹' s) = 0

Defined in: Mathlib.MeasureTheory.Constructions.Pi
Cited by: 3 results in Mathlib
Foundations: Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype MeasurableSpace MeasureTheory.SigmaFinite

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites21

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
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Fintypestatement and proof · cited by 7,736
Set.preimagestatement and proof · cited by 4,946
Set.univproof · cited by 3,945
MeasurableSetproof · cited by 3,075
MeasureTheory.SigmaFinitestatement and proof · cited by 526
Function.updateproof · cited by 502
Finset.mem_univproof · cited by 361

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.tendsto_eval_ae_aeproof · cited by 4
MeasureTheory.Measure.quasiMeasurePreserving_evalproof · cited by 3
MeasureTheory.Measure.pi_hyperplaneproof · cited by 2