The below image is an excerpt from Thomas Hawkins’ Lebesgue’s Theory of Integration: Its History and Development.
Following the excerpt, the author says in the next page that (R1) represents the “germs of (Jordan) measurability”. I am trying to understand this.
A set is Jordan measurable whenever the infimum of the sum of the measure of simple sets whose union covers it, equals the supremum of the sum of the measure of simple sets whose union is contained in it.
How does this connect to (R1)?
