Theorems · Theorem · probability
ProbabilityTheory.aemeasurable_of_mem_interior_integrableExpSet
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} {v : ℝ},
v ∈ interior (ProbabilityTheory.integrableExpSet X μ) → AEMeasurable X μIf the interior of the interval integrableExpSet X μ is nonempty,
then X is a.e. measurable.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- LT.lt.ne'proof · cited by 1,417
- Set.Iooproof · cited by 1,214
- AEMeasurablestatement · cited by 840
- interiorstatement and proof · cited by 714
- sub_ne_zeroproof · cited by 119
- half_posproof · cited by 83
- mem_interior_iff_mem_nhdsproof · cited by 82
- ProbabilityTheory.integrableExpSetstatement and proof · cited by 66
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.hasDerivAt_integral_pow_mul_expproof · cited by 3
- ProbabilityTheory.memLp_of_mem_interior_integrableExpSetproof · cited by 3
- ProbabilityTheory.memLp_tilted_mulproof · cited by 1