Theorems · Theorem · probability
MeasureTheory.AEStronglyMeasurable.memLp_truncation
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.AEStronglyMeasurable f μ →
∀ {A : ℝ} {p : ENNReal}, MeasureTheory.MemLp (ProbabilityTheory.truncation f A) p μ- Defined in
- Mathlib.Probability.StrongLaw
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- absproof · cited by 1,814
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- Filter.Eventually.of_forallproof · cited by 526
- MeasureTheory.MemLpstatement · cited by 457
- ProbabilityTheory.truncationstatement · cited by 23
- MeasureTheory.MemLp.of_boundproof · cited by 6
- MeasureTheory.AEStronglyMeasurable.truncationproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.strong_law_aux1proof · cited by 1
- MeasureTheory.AEStronglyMeasurable.integrable_truncationproof · cited by 1