Theorems · Theorem · probability
ProbabilityTheory.HasSubgaussianMGF.trim
∀ {Ω : Type u_1} {m mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X : Ω → ℝ} {c : NNReal} (hm : m ≤ mΩ),
Measurable X → ProbabilityTheory.HasSubgaussianMGF X c μ → ProbabilityTheory.HasSubgaussianMGF X c (μ.trim hm)- Defined in
- Mathlib.Probability.Moments.SubGaussian
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NNRealstatement and proof · cited by 4,310
- Measurablestatement and proof · cited by 1,499
- NNReal.toRealproof · cited by 1,260
- Real.expproof · cited by 871
- MeasureTheory.Measure.trimstatement and proof · cited by 286
- Measurable.stronglyMeasurableproof · cited by 47
- ProbabilityTheory.HasSubgaussianMGFstatement and proof · cited by 36
- Measurable.const_mulproof · cited by 19
- MeasureTheory.Integrable.trimproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasSubgaussianMGF.sum_of_hasCondSubgaussianMGFproof · cited by 2