  The theory of tournament limits and tournament kernels (often called
graphons) is developed by extending common notions for finite tournaments to
this setting; in particular we study transitivity and irreducibility of limits
and kernels. We prove that each tournament kernel and each tournament limit can
be decomposed into a direct sum of irreducible components, with transitive
components interlaced. We also show that this decomposition is essentially
unique.

Combinatorics;Probability