Measurement apparatus including an optical sensor, which performs repeatedly transmission measurements through moving sheet of paper or board at at least one wavelength band dominantly absorbed by water, at at least one wavelength band dominantly absorbed by cellulose. The apparatus also includes an X-ray sensor, which performs repeatedly transmission measurements through the moving sheet of paper or board with photons of electromagnetic radiation (1 keV to 10 keV). The apparatus comprises a data processing unit, which receives signals with information on intensities of the optical and X-ray radiations passed through the sheet from the optical sensor and the X-ray sensor, and determines, based on the information, all of the following of the moving sheet: the dry stuff content as a function of the cellulose mass per unit area of the sheet, water mass per unit area of the sheet and the ash mass per unit area of the sheet.