Once we've satified the sampling theorem we can theoretically reconstruct the function. This requires low-pass filtering the samples that are used to represent the image.

Remember the samples that we store in memory are points; they have no area only positions. It is this reconstruction filter that gives a pixel area.

Question: If what I say is true how can we just stick pixel values in our frame buffer and see a picture? If they were just points (like I claim) we would see anything.

The fact is that a CRT has a built in reconstruction filter. Most real world devices do because they do not have an infinite frequency response.

Each pixel illuminates a spot on the screen whose intensity fall off is well approximated by a gaussian.