The embedding functions of an intermediate space A into a Banach couple
(A0,A1) are defined as its embedding constants into the couples
(1αA0,1βA1), ∀α,β>0. Using these functions,
we study properties and interrelations of different intermediate spaces, give a new description of all real
interpolation spaces, and generalize the concept of weak-type interpolation to
any Banach couple to obtain new interpolation theorems.