Theorems · Theorem · measure theory
dimH_bUnion
∀ {ι : Type u_1} {X : Type u_2} [inst : EMetricSpace X] {s : Set ι},
s.Countable → ∀ (t : ι → Set X), dimH (⋃ i ∈ s, t i) = ⨆ i ∈ s, dimH (t i)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- ENNRealstatement and proof · cited by 9,879
- Set.Elemproof · cited by 7,166
- Set.iUnionstatement · cited by 2,483
- iSupstatement and proof · cited by 2,415
- Set.Countablestatement and proof · cited by 545
- EMetricSpacestatement and proof · cited by 242
- Encodableproof · cited by 140
- dimHstatement and proof · cited by 65
- Set.biUnion_eq_iUnionproof · cited by 41
- Set.Countable.toEncodableproof · cited by 22
- iSup_subtype''proof · cited by 18
Cited by4
Results whose statement or proof uses this declaration.
- dimH_image_le_of_locally_holder_onproof · cited by 2
- exists_mem_nhdsWithin_lt_dimH_of_lt_dimHproof · cited by 1
- dimH_countableproof · cited by 1
- dimH_sUnionproof · cited by 0