In our first go‐around, we decided what a measurable set was by fiat. More precisely, we defined the concept of σ‐algebra and then declared, “This is the σ‐algebra of measurable sets Now, in our new development, the point of view is different. Here we will understand measurable sets by more of a discovery method. And the measurable sets defined with our new technique will have all the desirable properties of a measure—including countable additivity.