Theorems · Theorem · statistics
ProbabilityTheory.minimaxRisk_of_isEmpty
∀ {Θ : Type u_1} {𝓧 : Type u_2} {𝓨 : Type u_3} {mΘ : MeasurableSpace Θ} {m𝓧 : MeasurableSpace 𝓧}
{m𝓨 : MeasurableSpace 𝓨} {ℓ : Θ → 𝓨 → ENNReal} {P : ProbabilityTheory.Kernel Θ 𝓧} [IsEmpty 𝓧],
ProbabilityTheory.minimaxRisk ℓ P = 0- Defined in
- Mathlib.Probability.Decision.Risk.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement and proof · cited by 9,879
- iSupproof · cited by 2,415
- iInfproof · cited by 1,690
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.lintegralproof · cited by 1,152
- IsEmptystatement and proof · cited by 759
- zero_applyproof · cited by 251
- iInf_congr_Propproof · cited by 218
- ProbabilityTheory.Kernel.compproof · cited by 129
- ProbabilityTheory.IsMarkovKernelproof · cited by 124
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