Theorems · Theorem · measure theory
MeasureTheory.Measure.ae_sum_eq
∀ {α : Type u_1} {ι : Type u_5} {m0 : MeasurableSpace α} [Countable ι] (μ : ι → MeasureTheory.Measure α),
MeasureTheory.ae (MeasureTheory.Measure.sum μ) = ⨆ i, MeasureTheory.ae (μ i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
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
- Filterstatement · cited by 8,121
- iSupstatement · cited by 2,415
- MeasureTheory.aestatement · cited by 2,352
- Countablestatement and proof · cited by 633
- MeasureTheory.Measure.sumstatement · cited by 121
- Filter.extproof · cited by 60
- MeasureTheory.Measure.ae_sum_iffproof · cited by 4
- Filter.mem_iSupproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_restrict_iUnion_eqproof · cited by 4
- MeasureTheory.AEStronglyMeasurable.sum_measureproof · cited by 2