[a, b]-F consists of countable open intervals. Call this group of open intervals g.

Let the maximum open interval in G be (daoa 1, b 1), and let i0 = [a, a 1], i 1 = [b 1, b].

Then the largest interval in G is removed from I0, the small part is called I00, and the large part is called I0 1.

In I 1, the largest interval in G is removed, and the small part is called I 10, and the large part is called I 1 1.

Extended data:

The theory of real variable function is a branch of mathematics that takes real variable function as the research object. It is the deepening and popularization of mathematical analysis, and studies the representation and approximation of functions and their local and global properties. In classical analysis, we mainly study functions with certain order smoothness. However, in the second half of the19th century, some questions were clearly put forward, hoping to be answered, involving a wider range of functions.

The relationship between curve length and surface area, the relationship between primitive function and integral, the relationship between integral and differential, the relationship between item-by-item integral and differential of series, and the properties of the function obtained from the limit process. The solution of these problems is very important to the development of mathematics, but it is beyond the scope of classical analysis. It was not until the end of 19 and the beginning of the 20th century that these problems were solved on the basis of set theory, which laid the foundation of modern real variable function theory.