  Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von
Neumann algebra $\mathcal M$ with respect to a faithful normal conditional
expectation $\Phi$. We give necessary and sufficient conditions for which
$\mathfrak A$ is maximal among the $\sigma$-weakly closed subalgebras of
$\mathcal M$. In addition, we show that a type 1 subdiagonal algebra in a
finite von Neumann algebra is automatically finite which gives a positive
answer of Arveson's finiteness problem in 1967 in type 1 case.
