On a result of Jessica Lin

In Theorem 1.5 of [5] an estimate from below is given for nonnegative supersolutions of parabolic equations in terms of the measure of the set where the right-hand side is less than $-1$. The given proof contains many interesting details which are certainly useful in many other situations. However, as long as the statement of Theorem 1.5 of \cite{JL} is concerned, it can be proved in a much shorter way, which we present here.