Construction
The discussion that follows parallels the most common expository approach to the Lebesgue integral. In this approach, the theory of integration has two distinct parts:
- A theory of measurable sets and measures on these sets.
- A theory of measurable functions and integrals on these functions.
The function whose integral is to be found is then approximated by certain so-called simple functions, whose integrals can be written in terms of the measure. The integral of the original function is then the limit of the integral of the simple functions.
Read more about this topic: Lebesgue Integration
Famous quotes containing the word construction:
“No real “vital” character in fiction is altogether a conscious construction of the author. On the contrary, it may be a sort of parasitic growth upon the author’s personality, developing by internal necessity as much as by external addition.”
—T.S. (Thomas Stearns)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“No construction stiff working overtime takes more stress and straining than we did just to stay high.”
—Gus Van Sant, U.S. screenwriter and director, and Dan Yost. Bob Hughes (Matt Dillon)