Theorems · Theorem · probability

ProbabilityTheory.Kernel.indep_of_indep_of_le_left

∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {m₁ m₂ m₃ _mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α},
  ProbabilityTheory.Kernel.Indep m₁ m₂ κ μ → m₃ ≤ m₁ → ProbabilityTheory.Kernel.Indep m₃ m₂ κ μ

Defined in: Mathlib.Probability.Independence.Kernel.Indep
Cited by: 5 results in Mathlib
Foundations: Depth 178 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.

Setproof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.ofPredproof · cited by 6,101
MeasurableSetproof · cited by 3,075
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
ProbabilityTheory.Kernel.Indepstatement and proof · cited by 42

Cited by5

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.indep_limsup_selfproof · cited by 5
ProbabilityTheory.Kernel.indep_of_indep_of_leproof · cited by 2
ProbabilityTheory.Kernel.Indep.indicator_const_indepFunproof · cited by 1
ProbabilityTheory.condIndep_of_condIndep_of_le_leftproof · cited by 0
ProbabilityTheory.indep_of_indep_of_le_leftproof · cited by 0