Solution
= Solution
Since $X_1-X_s$ is centered Gaussian with variance $1-s$,
$$
\mathbb E\int_0^1\frac{|X_1-X_s|}{1-s}\,ds
=C\int_0^1(1-s)^{-1/2}\,ds<\infty.
$$
<Fubini's theorem> therefore shows that the defining integral for $A_1$ is absolutely finite almost surely.