Neretin in [Izv. Ross. Akad. Nauk Ser. Mat. 77 (2013), pp. 95–108] constructed an analogue of the Hua measures on the infinite
p
p
-adic matrices
M
a
t
(
N
,
Q
p
)
\mathrm {Mat}\left (\mathbb {N},\mathbb {Q}_p\right )
. Bufetov and Qiu in [Compos. Math. 153 (2017), pp. 2482–2533] classified the ergodic measures on
M
a
t
(
N
,
Q
p
)
\mathrm {Mat}\left (\mathbb {N},\mathbb {Q}_p\right )
that are invariant under the natural action of
G
L
(
∞
,
Z
p
)
×
G
L
(
∞
,
Z
p
)
\mathrm {GL}(\infty ,\mathbb {Z}_p)\times \mathrm {GL}(\infty ,\mathbb {Z}_p)
. In this paper we solve the problem of ergodic decomposition for the
p
p
-adic Hua measures introduced by Neretin. We prove that the probability measure governing the ergodic decomposition has an explicit expression which identifies it with a Hall-Littlewood measure on partitions. Our arguments involve certain Markov chains.