Theorems · Theorem · dynamical systems
Dynamics.coverEntropyInf_eq_iSup_basis
∀ {X : Type u_1} [inst : UniformSpace X] {ι : Sort u_2} {p : ι → Prop} {s : ι → SetRel X X},
(uniformity X).HasBasis p s →
∀ (T : X → X) (F : Set X),
Dynamics.coverEntropyInf T F = ⨆ i, ⨆ (_ : p i), Dynamics.coverEntropyInfEntourage T F (s i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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Cites18
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
- LE.le.transproof · cited by 3,151
- iSupstatement · cited by 2,415
- le_reflproof · cited by 2,061
- UniformSpacestatement and proof · cited by 2,040
- ERealstatement · cited by 793
- uniformitystatement and proof · cited by 765
- Filter.HasBasisstatement and proof · cited by 604
- SetRelstatement and proof · cited by 581
- LE.le.antisymmproof · cited by 507
- Filter.HasBasis.mem_iffproof · cited by 193
- iSup₂_leproof · cited by 96
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