  We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of
independent functions on mutually exclusive subsets of the variables. We prove
that any such function is close to just a single function on a single subset.
  We also consider Boolean functions f:R^n->{-1,1} that are close, with respect
to any product distribution over R^n, to a sum of their variables. We prove
that any such function is close to one of the variables.
  Both our results are independent of the number of variables, but depend on
the variance of f. I.e., if f is \epsilon*Var(f)-close to a sum of independent
functions or random variables, then it is O(\epsilon)-close to one of the
independent functions or random variables, respectively. We prove that this
dependence on Var(f) is tight.
  Our results are a generalization of the Friedgut-Kalai-Naor Theorem [FKN'02],
which holds for functions f:{-1,1}^n->{-1,1} that are close to a linear
combination of uniformly distributed Boolean variables.
