The statistical transformation theory contains procedures for the computation of measurement probabilities, but requires for its completion a statement about the state-change due to the measurement process. We discuss and reject an ansatz suggested for this by J. von Neumann. We submit an ansatz for the state-change which is essentially identical to the ‘reduction of the wave function’. It permits a deepening of the concept of compatibility of measurements. Finally, measurements of states subject to con straints are considered.