Theorems · Theorem · measure theory

MeasureTheory.rnDeriv_tilted_left_self

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ} [MeasureTheory.SigmaFinite μ],
  AEMeasurable f μ →
    (μ.tilted f).rnDeriv μ =ᵐ[μ] fun x => ENNReal.ofReal (Real.exp (f x) / ∫ (x : α), Real.exp (f x) ∂μ)

Defined in: Mathlib.MeasureTheory.Measure.Tilted
Cited by: 1 results in Mathlib
Foundations: Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SigmaFinite

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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
mul_oneproof · cited by 3,885
MeasureTheory.aestatement · cited by 2,352
Filter.EventuallyEqstatement · cited by 1,912
MeasureTheory.integralstatement and proof · cited by 1,779
Filter.univ_mem'proof · cited by 1,672
Filter.mp_memproof · cited by 1,537
Real.expstatement and proof · cited by 871
ENNReal.ofRealstatement and proof · cited by 863

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.log_rnDeriv_tilted_left_selfproof · cited by 0