  We give a positive answer to the question of K. Bouras [`Almost
Dunford-Pettis sets in Banach lattices', \textit{Rend. Circ. Mat. Palermo (2)}
\textbf{ 62} (2013), 227--236] concerning weak compactness of almost
Dunford-Pettis sets in Banach lattices. That is, every almost Dunford-Pettis
set in a Banach lattice $E$ is relatively weakly compact if, and only if, $E$
is a $KB$-space.
