  S.Janson [Poset limits and exchangeable random posets, Combinatorica 31
(2011), 529--563] defined limits of finite posets in parallel to the emerging
theory of limits of dense graphs.
  We prove that each poset limit can be represented as a kernel on the unit
interval with the standard order, thus answering an open question of Janson. We
provide two proofs: real-analytic and combinatorial. The combinatorial proof is
based on a Szemeredi-type Regularity Lemma for posets which may be of
independent interest.
  Also, as a by-product of the analytic proof, we show that every atomless
ordered probability space admits a measure-preserving and almost
order-preserving map to the unit interval.
