Theorems · Theorem · dynamical systems
MeasureTheory.Conservative.id
∀ {α : Type u_1} [inst : MeasurableSpace α] (μ : MeasureTheory.Measure α), MeasureTheory.Conservative id μThe identity map is conservative w.r.t. any measure.
- Defined in
- Mathlib.Dynamics.Ergodic.Conservative
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetproof · cited by 3,075
- MeasureTheory.Measure.QuasiMeasurePreservingproof · cited by 101
- MeasureTheory.nonempty_of_measure_ne_zeroproof · cited by 22
- MeasureTheory.Conservativestatement · cited by 19
- MeasureTheory.Measure.QuasiMeasurePreserving.idproof · cited by 14
- Function.iterate_idproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Conservative.iterateproof · cited by 0