Theorems · Theorem · dynamical systems

Dynamics.IsDynCoverOf.coverEntropyEntourage_le_log_card_div

∀ {X : Type u_1} {T : X → X} {U : SetRel X X} {F : Set X} {n : ℕ},
  Set.MapsTo T F F →
    ∀ [U.IsSymm],
      n ≠ 0 →
        ∀ {s : Finset X},
          Dynamics.IsDynCoverOf T F U n ↑s → Dynamics.coverEntropyEntourage T F (U.comp U) ≤ (↑s.card).log / ↑n

Defined in: Mathlib.Dynamics.TopologicalEntropy.CoverEntropy
Cited by: 1 results in Mathlib
Foundations: Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SetRel.IsSymm

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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
Finsetstatement and proof · cited by 13,712
ENNRealstatement · cited by 9,879
SetLike.coestatement and proof · cited by 8,199
LE.le.transproof · cited by 3,151
Finset.cardstatement and proof · cited by 2,327
ERealstatement · cited by 793
Set.MapsTostatement and proof · cited by 732
SetRelstatement and proof · cited by 581
Nat.cast_nonneg'proof · cited by 245
SetRel.compstatement · cited by 136
ENat.toENNRealproof · cited by 103

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Dynamics.coverEntropyEntourage_finite_of_isCompact_invariantproof · cited by 0