For τ a piecewise C2 transformation, we present a method for obtaining an upper bound for the number of independent absolutely continuous measures invariant under τ.
Let τ = [0,1] and let τ:I→ J be a piecewise C2 transformation with infI1 |dτ/dx| > 1, where I1 = I-P and P denotes the points of discontinuity of τ and τ′