Absolute Continuity
In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using Lebesgue integration and absolute continuity. For real-valued functions on the real line two interrelated notions appear, absolute continuity of functions and absolute continuity of measures. These two notions are generalized in different directions. The usual derivative of a function is related to the Radon–Nikodym derivative, or density, of a measure.
Read more about Absolute Continuity: Absolute Continuity of Functions, Relation Between The Two Notions of Absolute Continuity
Famous quotes containing the words absolute and/or continuity:
“In our science and philosophy, even, there is commonly no true and absolute account of things. The spirit of sect and bigotry has planted its hoof amid the stars. You have only to discuss the problem, whether the stars are inhabited or not, in order to discover it.”
—Henry David Thoreau (1817–1862)
“The dialectic between change and continuity is a painful but deeply instructive one, in personal life as in the life of a people. To “see the light” too often has meant rejecting the treasures found in darkness.”
—Adrienne Rich (b. 1929)