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:
“There is an inner world; and a spiritual faculty of discerning it with absolute clearness, nay, with the most minute and brilliant distinctness. But it is part of our earthly lot that it is the outer world, in which we are encased, which is the lever that brings that spiritual faculty into play.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)
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