This paper was written using the investigative method. It is divided into three main parts, the first two being closely connected, and the second containing more examples of generalisations of the first. We could say that this paper was made on multiple levels, such that every next level contains and summarises the previous one. In this way, we can say that from the very beginning, from the surfaces of polygons to the volumes of polyedars we rise up the chain of knowledge all the way to measurable sets. In the end, all of this will be contained in sets which we call Lebesgue sets. This paper therebly sets out to make a link between lower and higher level mathematics, and all of it is supported with numerous examples and images that provide easier understanding of the paper.