Helper

zero_centropy1_point_mass

File dumas2017dual/lib/extra_entropy.v

Section zero_centropy_eq_point_mass

Type Lemma

Proof Lines 25

Signature

Lemma zero_centropy1_point_mass (V W T : finType) (P : R.-fdist T) (Y : {RV P -> V}) (Z : {RV P -> W}) (y : V) (HPrYeq0 : `Pr[Y = y] != 0) (Hy_centropy_zero : - (\sum_(b in W) \Pr_`p_[% Z, Y][[set b] | [set y]] * log \Pr_`p_[% Z, Y][[set b] | [set y]]) = 0) : exists z : W, `Pr[Z = z | Y = y] = 1.

Description

Helper: If the conditional entropy at y equals zero (as a Prop equality = 0) then there exists z with Pr[Z = z | Y = y] = 1.

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