Theorems · Definition · statistics

ProbabilityTheory.IsArgminEstimator.recOn

{Θ : Type u_1} →
  {𝓧 : Type u_2} →
    {mΘ : MeasurableSpace Θ} →
      {m𝓧 : MeasurableSpace 𝓧} →
        [inst : StandardBorelSpace Θ] →
          [inst_1 : Nonempty Θ] →
            {𝓨 : Type u_4} →
              [inst_2 : MeasurableSpace 𝓨] →
                {ℓ : Θ → 𝓨 → ENNReal} →
                  {P : ProbabilityTheory.Kernel Θ 𝓧} →
                    [inst_3 : ProbabilityTheory.IsFiniteKernel P] →
                      {π : MeasureTheory.Measure Θ} →
                        [inst_4 : MeasureTheory.IsFiniteMeasure π] →
                          {f : 𝓧 → 𝓨} →
                            {motive : ProbabilityTheory.IsArgminEstimator ℓ P π f → Sort u} →
                              (t : ProbabilityTheory.IsArgminEstimator ℓ P π f) →
                                ((measurable : Measurable f) →
                                    (property :
                                        ∀ᵐ (x : 𝓧) ∂π.bind ⇑P,
                                          ∫⁻ (θ : Θ), ℓ θ (f x) ∂(ProbabilityTheory.posterior P π) x =
                                            ⨅ y, ∫⁻ (θ : Θ), ℓ θ y ∂(ProbabilityTheory.posterior P π) x) →
                                      motive ⋯) →
                                  motive t

Defined in

Mathlib.Probability.Decision.BayesEstimator

Cited by

0 results in Mathlib

Foundations

Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

StandardBorelSpaceNonemptyMeasurableSpaceProbabilityTheory.IsFiniteKernelMeasureTheory.IsFiniteMeasure