The 
-norm
of an essentially bounded measurable function 
is
where the essential supremum is taken with respect to the underlying measure. For a finite vector 
, equivalently a function
on a finite set with counting measure, this reduces
to
This finite-dimensional vector norm is also called the infinity norm or maximum norm. The vector norm
is implemented in the Wolfram
Language as Norm[x,
Infinity].
See also
Essential Supremum,
Infinity Norm,
L1-Norm,
L2-Norm,
Maximum Absolute Row Sum Norm,
Vector
Norm
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References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
pp. 1114-1125, 2000.Horn, R. A. and Johnson, C. R. "Norms
for Vectors and Matrices." Ch. 5 in Matrix
Analysis. Cambridge, England: Cambridge University Press, 1990.Rudin,
W. Real
and Complex Analysis, 3rd ed. New York: McGraw-Hill, 1987.Referenced
on Wolfram|Alpha
L^infty-Norm
Cite this as:
Weisstein, Eric W. "L^infty-Norm." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/L-Infinity-Norm.html
Subject classifications
