Theorems · Theorem · functional analysis
MeasureTheory.AEFinStronglyMeasurable.exists_measurableSet_measure_pos_lt_top
∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α}
{f : α → E}, MeasureTheory.AEFinStronglyMeasurable f μ → ¬f =ᵐ[μ] 0 → ∃ s, MeasurableSet s ∧ 0 < μ s ∧ μ s < ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- MeasurableSetstatement · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyEq.transproof · cited by 123
- MeasureTheory.AEFinStronglyMeasurablestatement and proof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.nontrivial_Lp_real_of_nontrivial_Lpproof · cited by 1