Theorems · Theorem · probability

ProbabilityTheory.integrable_pow_abs_mul_exp_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) →
    ∀ (n : ℕ), MeasureTheory.Integrable (fun ω => |X ω| ^ n * Real.exp (v * X ω)) μ

If v belongs to the interior of the interval integrableExpSet X μ, then |X| ^ n * exp (v * X) is integrable for all n : ℕ.

Defined in

Mathlib.Probability.Moments.IntegrableExpMul

Cited by

1 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound