✦ LIBER ✦

RIESZ Representation of p-Linear Forms on C(X)

✍ Scribed by Winfried Stute

Publisher: John Wiley and Sons
Year: 1984
Tongue: English
Weight: 213 KB
Volume: 115
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19841150120

No coin nor oath required. For personal study only.

✦ Synopsis

In t h i s paper we prove a RIESZ representation theorem for continuous ~nultilinear f o r m on C ( X ) , the space of real-valued continuous functions on a compact HAUSDORFF space X . Our main result states that every nonnegative (sup-norm) continuous p-linear form K on C ( S ) has a representation k'(gl, ..a, gp) = j g 1 8 *-. @ g p a $71, a * . , g,€Q(-w

for some nonnegative (finite) measure Q 1 @ex. Here ear denotes the a-field of HAIRE sets on X, and g1 8 ... @ g p is the tensor product of gl, ..., g p defined by g1 8 .... @gp(zI, ..., x p ) =gl(rl) .... g p ( x p ) . Froin this we can fully describe the class

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