Lifting theorems are theorems that bound the communication complexity
of a composed function f\circ g^{n} in terms of the query complexity
of f and the communication complexity of g. Such theorems
constitute a powerful generalization of direct-sum theorems for g,
and have seen numerous applications in recent years.

We prove a new lifting theorem that works for every two functions f,g
such that the discrepancy of g is at most inverse polynomial in
the input length of f. Our result is a significant generalization
of the known direct-sum theorem for discrepancy, and extends the range
of inner functions g for which lifting theorems hold.