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Theorems · Theorem · dynamical systems

Dynamics.coverEntropyEntourage_le_coverEntropyInfEntourage

∀ {X : Type u_1} {T : X → X} {U : SetRel X X} {F : Set X},
  Set.MapsTo T F F →
    ∀ [U.IsSymm], Dynamics.coverEntropyEntourage T F (U.comp U) ≤ Dynamics.coverEntropyInfEntourage T F U
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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Dynamics.coverEntropyInf_eq_coverEntropy · cited by 0Dynamics.coverEntropyInf_…Set · cited by 53352SetEReal · cited by 793ERealSet.MapsTo · cited by 732Set.MapsToSetRel · cited by 581SetRelSetRel.comp · cited by 136SetRel.compFilter.eventually_atTop · cited by 112Filter.eventually_atTopSetRel.IsSymm · cited by 93SetRel.IsSymmFilter.isCobounded_ge_of_top · cited by 38Filter.isCobounded_ge_of_…Dynamics.coverEntropyEntourage · cited by 20Dynamics.coverEntropyEnto…Dynamics.coverEntropyInfEntourage · cited by 15Dynamics.coverEntropyInfE…Filter.le_liminf_of_le · cited by 9Filter.le_liminf_of_leDynamics.coverEntropyEntourage_le_log_coverMincard_div · cited by 2Dynamics.coverEntropyEnto…Dynamics.coverEntropyEntourag…CITED BYCITES

Cites12

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