We study poset limits given by sequences of finite interval orders or, as a
special case, finite semiorders. In the interval order case, we show that every
such limit can be represented by a probability measure on the space of closed
subintervals of [0,1], and we define a subset of such measures that yield a
unique representation. In the semiorder case, we similarly find unique
representations by a class of distribution functions.Comment: 18 page
