Theorems · Theorem · measure theory
MeasureTheory.mem_closedCompactCylinders
∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] (t : Set ((i : ι) → X i)),
t ∈ MeasureTheory.closedCompactCylinders X ↔ ∃ s S, IsClosed S ∧ IsCompact S ∧ t = MeasureTheory.cylinder s S- Cited by
- 4 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- MeasureTheory.cylinderstatement and proof · cited by 49
- MeasureTheory.closedCompactCylindersstatement · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.closedCompactCylinders.isClosedproof · cited by 1
- MeasureTheory.closedCompactCylinders.eq_cylinderproof · cited by 1
- MeasureTheory.closedCompactCylinders.isCompactproof · cited by 0
- MeasureTheory.cylinder_mem_closedCompactCylindersproof · cited by 0