Oscillation, convergence, and stability of linear delay differential equations

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 $c$ locally integrable any sign, $\tau(t)\leq t$ Lebesgue measurable, $\lim_{t\rightarrow\infty}\tau(t)=\infty$, we obtain sharp results, relating speed stability. We thus unify classical results Myshkis Lillo. also generalise $3/2-$stability criterion to case measurable parameters, improving $1+1/e$ $3/2$ constant.