Layer cake representation
In mathematics, the layer cake representation of a non-negative, real-valued measurable function f defined on n-dimensional Euclidean space is the formula
for all , where denotes the indicator function of a subset and denotes the super-level set
The layer cake representation follows easily from observing that
and then using the formula
The layer cake representation takes its name from the representation of the value as the sum of contributions from the "layers" : "layers"/values t below contribute to the integral, while values t above do not.
See also
References
- Gardner, Richard J. (2002). "The Brunn–Minkowski inequality". Bull. Amer. Math. Soc. (N.S.). 39 (3): 355–405 (electronic). doi:10.1090/S0273-0979-02-00941-2.
- Lieb, Elliott; Loss, Michael (2001). Analysis. Graduate Studies in Mathematics. 14 (2nd ed.). American Mathematical Society. ISBN 978-0821827833.
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