Theorems · Theorem · measure theory
Continuous.ae_eq_iff_eq
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {m : MeasurableSpace X} [inst_1 : TopologicalSpace Y]
[T2Space Y] (μ : MeasureTheory.Measure X) [μ.IsOpenPosMeasure] {f g : X → Y},
Continuous f → Continuous g → (f =ᵐ[μ] g ↔ f = g)- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Continuousstatement and proof · cited by 2,592
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- T2Spacestatement and proof · cited by 1,351
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
- Filter.EventuallyEq.rflproof · cited by 55
- MeasureTheory.Measure.eq_of_ae_eqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.toLp_injproof · cited by 1
- MeasureTheory.lintegral_eq_zero_of_isMulLeftInvariantproof · cited by 0
- SchwartzMap.injective_toLpproof · cited by 0
- MeasureTheory.lintegral_eq_zero_of_isAddLeftInvariantproof · cited by 0