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Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.iterate

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {f : α → α},
  MeasureTheory.MeasurePreserving f μ μ → ∀ (n : ℕ), MeasureTheory.MeasurePreserving f^[n] μ μ
Defined in
Mathlib.Dynamics.Ergodic.MeasurePreserving
Cited by
6 results in Mathlib
Foundations
Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_measure_univ_lt_mul_measure · cited by 1MeasurePreserving.exists_…MeasureTheory.MeasurePreserving.smulInvariantMeasure_iterateMulAct · cited by 1MeasurePreserving.smulInv…MeasureTheory.MeasurePreserving.vaddInvariantMeasure_iterateAddAct · cited by 1MeasurePreserving.vaddInv…MeasureTheory.Lp.compMeasurePreserving_iterate · cited by 0Lp.compMeasurePreserving_…MeasureTheory.AEEqFun.compMeasurePreserving_iterate · cited by 0AEEqFun.compMeasurePreser…MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le · cited by 0MeasurePreserving.measure…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureNat.iterate · cited by 740Nat.iterateMeasureTheory.MeasurePreserving · cited by 259MeasureTheory.MeasurePres…MeasurePreserving.iterateCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.