Lebesgue measure

Lebesgue measure is a way of measuring how much "space" a certain shape takes up. It helps us to figure out the size of shapes on a flat piece of paper, like a circle, square or rectangle. For example, if we have a circle that takes up 1 square inch of paper, a Lebesgue measure can tell us the circle's size without us having to measure it. To use the Lebesgue measure we need to think about the shape in terms of small squares. The measure is based on the number of small squares it takes up. For example, if a shape takes up 10 small squares, it would have a Lebesgue measure of 10.