Definition
A partition of an interval is a finite sequence of values xi such that
Each interval is called a subinterval of the partition. Let ƒ:→R be a bounded function, and let
be a partition of . Let
The upper Darboux sum of ƒ with respect to P is
The lower Darboux sum of ƒ with respect to P is
The upper Darboux integral of ƒ is
The lower Darboux integral of ƒ is
If Uƒ = Lƒ, then we say that ƒ is Darboux-integrable and set
the common value of the upper and lower Darboux integrals.
Read more about this topic: Darboux Integral
Famous quotes containing the word definition:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)