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Singular Function: Continuous Function, Measure, Derivative -

English
2026-03-20
€207.26 €259.07

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High Quality Content by WIKIPEDIA articles! In mathematics, a singular function is any function f defined on the interval [a, b] that has the following properties: f is continuous on [a, b]. there exists a set N of measure 0 such that for all x outside of N the derivative f ¿(x) exists and is zero, that is, the derivative of f vanishes almost everywhere. f is nondecreasing on [a, b]. f(a) < f(b). A standard ... Full description

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High Quality Content by WIKIPEDIA articles! In mathematics, a singular function is any function f defined on the interval [a, b] that has the following properties: f is continuous on [a, b]. there exists a set N of measure 0 such that for all x outside of N the derivative f ¿(x) exists and is zero, that is, the derivative of f vanishes almost everywhere. f is nondecreasing on [a, b]. f(a) < f(b). A standard example of a singular function is the Cantor function, which is sometimes called the devil's staircase (a term also used for singular functions in general). There are, however, other functions that have been given that name. One is defined in terms of the circle map.

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131189135
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€207.26 €259.07