Helper

centropy_jcond_determined_fibers

File dumas2017dual/entropy_fiber/entropy_fiber.v

Section conditional_entropy_with_functional_constraint

Type Lemma

Proof Lines 50

Signature

Lemma centropy_jcond_determined_fibers (fiber_card : nat) : (forall y z, `Pr[[% Y, Z] = (y, z)] != 0 -> #|[set x' | g x' y == z]| = fiber_card) -> (0 < fiber_card)%N -> `H(X | [% Y, Z]) = log (fiber_card%:R : R).

Description

When fibers have constant cardinality and X is uniform over each fiber, the conditional entropy is log(fiber_card). Joint conditioning version.

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