Theorems · Theorem · measure theory

MeasureTheory.setLIntegral_tilted

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.SFinite μ] (f : α → ℝ)
  (g : α → ENNReal) (s : Set α),
  ∫⁻ (x : α) in s, g x ∂μ.tilted f =
    ∫⁻ (x : α) in s, ENNReal.ofReal (Real.exp (f x) / ∫ (x : α), Real.exp (f x) ∂μ) * g x ∂μ

Defined in

Mathlib.MeasureTheory.Measure.Tilted

Cited by

0 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFinite