Theorems · Definition · statistics

ProbabilityTheory.HasArgminEstimator.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] →
                          {motive : ProbabilityTheory.HasArgminEstimator ℓ P π → Sort u} →
                            (t : ProbabilityTheory.HasArgminEstimator ℓ P π) →
                              ((exists_isArgminEstimator : ∃ f, ProbabilityTheory.IsArgminEstimator ℓ P π f) →
                                  motive ⋯) →
                                motive t

Defined in

Mathlib.Probability.Decision.BayesEstimator

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

StandardBorelSpaceNonemptyMeasurableSpaceProbabilityTheory.IsFiniteKernelMeasureTheory.IsFiniteMeasure