Theorems · Theorem · probability
ProbabilityTheory.convex_integrableExpSet
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
Convex ℝ (ProbabilityTheory.integrableExpSet X μ)integrableExpSet X μ is a convex subset of ℝ (it is an interval).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 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
- one_mulproof · cited by 2,841
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- add_commproof · cited by 1,535
- add_le_addproof · cited by 666
- Convexstatement · cited by 551
- add_mulproof · cited by 363
- mul_le_mul_of_nonneg_leftproof · cited by 361
- ProbabilityTheory.integrableExpSetstatement and proof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.eqOn_complexMGF_of_mgf'proof · cited by 1