Theorems · Theorem · measure theory
IsCountablySpanning.pi
∀ {ι : Type u_1} {α : ι → Type u_2} [Finite ι] {C : (i : ι) → Set (Set (α i))},
(∀ (i : ι), IsCountablySpanning (C i)) → IsCountablySpanning (Set.univ.pi '' Set.univ.pi C)Boxes of countably spanning sets are countably spanning.
- Defined in
- Mathlib.MeasureTheory.MeasurableSpace.Pi
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites15
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.imagestatement · cited by 5,609
- Set.univstatement and proof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- Set.iUnionproof · cited by 2,483
- Set.pistatement and proof · cited by 405
- Set.mem_image_of_memproof · cited by 371
- Encodableproof · cited by 140
- Encodable.decodeproof · cited by 77
- Set.pi_univproof · cited by 14
- nonempty_encodableproof · cited by 13
- IsCountablySpanningstatement and proof · cited by 12
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