A linear functional defined on a subspace of a vector space 
and which is dominated by a sublinear
function defined on 
has a linear extension which is also dominated by the sublinear
function.
Hahn-Banach Theorem
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References
Casti, J. L. "The Hahn-Banach Theorem." Ch. 4 in Five More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of 20th-Century Mathematics. New York: Wiley, pp. 155-205, 2000.Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.Referenced on Wolfram|Alpha
Hahn-Banach TheoremCite this as:
Weisstein, Eric W. "Hahn-Banach Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hahn-BanachTheorem.html