Helper

jfdist_cond_entropy_zero

File dumas2017dual/lib/extra_entropy.v

Section zero_centropy_eq_point_mass

Type Lemma

Proof Lines 15

Signature

Lemma jfdist_cond_entropy_zero (V W T : finType) (P : R.-fdist T) (Y : {RV P -> V}) (Z : {RV P -> W}) (y : V) (Hy_marginal : (`p_[% Y, Z])`1 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) : let cond_dist := jfdist_cond0 `p_[% Y, Z] y Hy_marginal in `H cond_dist = 0.

Description

Helper: Conditional distribution has zero entropy when centropy1 is zero

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