  There is a close connection between stability and oscillation of delay
differential equations. For the first-order equation $$
x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of
any sign, $\tau(t)\leq t$ is Lebesgue measurable,
$\lim_{t\rightarrow\infty}\tau(t)=\infty$, we obtain sharp results, relating
the speed of oscillation and stability. We thus unify the classical results of
Myshkis and Lillo. We also generalise the $3/2-$stability criterion to the case
of measurable parameters, improving $1+1/e$ to the sharp $3/2$ constant.
