Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_self
∀ {α : Type u_1} {m : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ],
μ.rnDeriv μ =ᵐ[μ] fun x => 1- Cited by
- 6 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- add_zeroproof · cited by 2,707
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.Measure.withDensityproof · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.measurable_rnDerivproof · cited by 75
- MeasureTheory.Measure.singularPartproof · cited by 71
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_add_selfproof · cited by 2
- MeasureTheory.Measure.rnDeriv_eq_one_iff_eqproof · cited by 2
- MeasureTheory.llr_selfproof · cited by 1
- MeasureTheory.rnDeriv_tilted_left_selfproof · cited by 1
- MeasureTheory.Measure.rnDeriv_self_addproof · cited by 1
- ProbabilityTheory.Kernel.rnDeriv_selfproof · cited by 0