  We consider approximation problems for a special space of d variate
functions. We show that the problems have small number of active variables, as
it has been postulated in the past using concentration of measure arguments. We
also show that, depending on the norm for measuring the error, the problems are
strongly polynomially or quasi-polynomially tractable even in the model of
computation where functional evaluations have the cost exponential in the
number of active variables.
