Theorems · Theorem · measure theory

IsCountablySpanning.prod

∀ {α : Type u_1} {β : Type u_2} {C : Set (Set α)} {D : Set (Set β)},
  IsCountablySpanning C → IsCountablySpanning D → IsCountablySpanning (Set.image2 (fun x1 x2 => x1 ×ˢ x2) C D)

Rectangles of countably spanning sets are countably spanning.

Defined in: Mathlib.MeasureTheory.MeasurableSpace.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
Set.univproof · cited by 3,945
Set.iUnionproof · cited by 2,483
SProd.sprodstatement and proof · cited by 1,750
Set.image2statement · cited by 311
Nat.unpairproof · cited by 67
Set.mem_image2_of_memproof · cited by 40
Set.univ_prod_univproof · cited by 32
IsCountablySpanningstatement and proof · cited by 12
Set.iUnion_unpair_prodproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.ext_prod₃proof · cited by 1