= Solution
Use the paper's notation $F$ for the <survivor function>, not for a cumulative distribution function. For a nonnegative continuous event time,
$$
\boxed{F(t)=\mathbb P(T>t),\qquad h(t)=\lim_{\varepsilon\downarrow0}\frac{\mathbb P(t<T\le t+\varepsilon\mid T>t)}{\varepsilon},\qquad H(t)=\int_0^t h(s)ds.}
$$
The <hazard function> is defined where survival is positive, and the last expression is the <integrated hazard>. These definitions assume the usual absolutely continuous <survival distribution> so that the displayed density and <hazard> derivatives exist almost everywhere.
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