  A classical result of J.-L. Lions asserts that if a solution to the
Navier-Stokes equations is such that: (i) it is in the Leray-Hopf class, and
(ii) belongs to $L^4(0,T;L^4)$, then it must satisfy the energy equality in the
time interval $[0,T]$. In this note we show that assumption (i) is not
necessary.
