OAI/GroupTheory/PolycyclicRecognition/Algebra/ConditionalKernelFiber.lean
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Conditional probabilities preserve factor observables
Every measurable observable of the conditioning factor is almost surely constant under almost every component, at its value on that component.
- theorem
OAI.PolycyclicRecognition.factorConditionalKernel_fiberline 26Source documentation
A factor observable retains its value under the conditional probability.
theorem factorConditionalKernel_fiber : ∀ᵐ y ∂μ.map f, ∀ᵐ x ∂factorConditionalKernel μ f hf y, h (f x) = h y := by …