Theorems · Definition · probability

ProbabilityTheory.Kernel.IsIrreducible.casesOn

{α : Type u_1} →
  {mα : MeasurableSpace α} →
    {φ : MeasureTheory.Measure α} →
      {κ : ProbabilityTheory.Kernel α α} →
        {motive : ProbabilityTheory.Kernel.IsIrreducible φ κ → Sort u} →
          (t : ProbabilityTheory.Kernel.IsIrreducible φ κ) →
            ((irreducible : ∀ ⦃A : Set α⦄, MeasurableSet A → φ A > 0 → ∀ (a : α), ∃ n, ((κ ^ n) a) A > 0) → motive ⋯) →
              motive t

Defined in: Mathlib.Probability.Kernel.Irreducible
Cited by: 1 results in Mathlib
Foundations: Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
MeasurableSetstatement and proof · cited by 3,075
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
ProbabilityTheory.Kernel.IsIrreduciblestatement and proof · cited by 3

Cited by1

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ProbabilityTheory.Kernel.isIrreducible_iffproof · cited by 0