Theorems · Theorem · dynamical systems
PreErgodic.smul_measure
∀ {α : Type u_1} {m : MeasurableSpace α} {f : α → α} {μ : MeasureTheory.Measure α} {R : Type u_2}
[inst : SMul R ENNReal] [inst_1 : IsScalarTower R ENNReal ENNReal], PreErgodic f μ → ∀ (c : R), PreErgodic f (c • μ)- Defined in
- Mathlib.Dynamics.Ergodic.Ergodic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SMulIsScalarTower
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.preimageproof · cited by 4,946
- IsScalarTowerstatement and proof · cited by 3,896
- MeasurableSetproof · cited by 3,075
- PreErgodicstatement and proof · cited by 19
- PreErgodic.aeconst_setproof · cited by 7
- Filter.EventuallyConst.antiproof · cited by 2
- MeasureTheory.Measure.ae_smul_measure_leproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- QuasiErgodic.smul_measureproof · cited by 0
- Ergodic.smul_measureproof · cited by 0