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:
“The appalling thing is the degree of charity women are capable of. You see it all the time ... love lavished on absolute fools. Love’s a charity ward, you know.”
—Lawrence Durrell (1912–1990)
“There is never a beginning, there is never an end, to the inexplicable continuity of this web of God, but always circular power returning into itself.”
—Ralph Waldo Emerson (1803–1882)