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Riesz's Theorem


Every continuous linear functional U[f] for f in C[a,b] can be expressed as a Stieltjes integral

 U[f]=int_a^bf(x)dw(x),

where w(x) is determined by U and is of bounded variation on [a,b].


See also

Stieltjes Integral

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References

Kestelman, H. "Riesz's Theorem." §11.5 in Modern Theories of Integration, 2nd rev. ed. New York: Dover, pp. 265-269, 1960.

Referenced on Wolfram|Alpha

Riesz's Theorem

Cite this as:

Weisstein, Eric W. "Riesz's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RieszsTheorem.html

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