resolution of the thickness a processing or sheet treating device 7 is provided which has a local effect on the roller 4 by creating a temperature change the temperature change is provided for example by using hot or cold air jets infrared heating or an inductive heating of the roller 4 all of these methods of affecting a temperature change are well known in the art the sheet treating device 7 has a number of zones 8 each of which can be regulated separately from the rest of the zones 8 for example each zone 8 may have its own air jet which blows air that has been adjusted to the appropriate temperature onto the surface of the roller 4 one zone 8 therefore affects a single strip 9 of the web 2 which is cross hatched in fig1 for clarification a stationary measuring bridge instrument 10 measures the effect of the sheet treating device 7 and is positioned downstream of the roller gap 6 in the direction of movement 3 of the web 2 in lieu of the measuring bridge 10 shown in fig1 a traversing measurement sensor can also be provided which continuously measures the thickness of the web 2 as the sensor is moved back and forth across the web 2 in a transverse direction i e in the direction indicated by arrow 22 in fig2 regardless of the measuring instrument used the thickness of the web 2 is measured at a number of points which is greater than the number.