Lemma 6.8
(Submodularity for sums)
.
Assuming that:
X
,
Y
,
Z
are independent
G
-valued random variables
Then
H
[
X
+
Y
+
Z
]
+
H
[
Z
]
≤
H
[
X
+
Z
]
+
H
[
Y
+
Z
]
.