  We revisit Kellerer's Theorem, that is, we show that for a family of real
probability distributions $(\mu_t)_{t\in [0,1]}$ which increases in convex
order there exists a Markov martingale $(S_t)_{t\in[0,1]}$ s.t.\ $S_t\sim
\mu_t$.
  To establish the result, we observe that the set of martingale measures with
given marginals carries a natural compact Polish topology. Based on a
particular property of the martingale coupling associated to Root's embedding
this allows for a relatively concise proof of Kellerer's theorem.
  We emphasize that many of our arguments are borrowed from Kellerer
\cite{Ke72}, Lowther \cite{Lo07}, and Hirsch-Roynette-Profeta-Yor
\cite{HiPr11,HiRo12}.
