Definition
The construction is based on the Henstock or gauge integral, however Pfeffer proved that the integral, at least in the one dimensional case, is less general than the Henstock integral. It relies on what Pfeffer refers to as a set of bounded variation, this is equivalent to a Caccioppoli set. The Riemann sums of the Pfeffer integral are taken over partitions made up of such sets, rather than intervals as in the Riemann or Henstock integrals. A gauge is used, exactly as in the Henstock integral, except that the gauge function may be zero on a negligible set.
Read more about this topic: Pfeffer Integral
Famous quotes containing the word definition:
“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)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)