We study theories of spaces of random variables: first, we consider random
variables with values in the interval [0,1], then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type