Theorems · Theorem · general topology
Metric.thickening_iUnion
∀ {ι : Sort u_1} {α : Type u} [inst : PseudoEMetricSpace α] (δ : ℝ) (f : ι → Set α),
Metric.thickening δ (⋃ i, f i) = ⋃ i, Metric.thickening δ (f i)- Defined in
- Mathlib.Topology.MetricSpace.Thickening
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- Set.iUnionstatement and proof · cited by 2,483
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofRealproof · cited by 863
- Metric.infEDistproof · cited by 147
- Metric.thickeningstatement · cited by 130
- Set.ofPred_existsproof · cited by 23
- Metric.infEDist_iUnionproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasureproof · cited by 1
- Metric.thickening_biUnionproof · cited by 0