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.

  1. theorem OAI.PolycyclicRecognition.factorConditionalKernel_fiber line 26

    Source 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
    …

    Mentions: OAI.PolycyclicRecognition.factorConditionalKernel