  A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to
field extensions. This theorem was known to be valid only in separable
extensions, and it was a conjecture of Hou that it should be valid for all
extensions. We give an alternative proof of the theorem that also holds in the
non-separable case, thus solving Hou's conjecture. This result is a consequence
of a strengthening of Hou et al.'s theorem that is a transposition to extension
fields of an addition theorem of Balandraud.
