I.1. Physical motivation. From [St]: consider a function T (x) as representing the value of a physical variable at a particular point x in space. Is this a realistic thing to do? What can you measure? Suppose T (x) represents temperature at a point x in a room. You can measure the temperature with a thermometer, placing the bulb at the point x. Unlike the point, the bulb has nonzero size, so wh...