Signed quasi-measures and dimension theory

Grubb, D.

doi:10.1090/S0002-9939-99-05093-5

Signed quasi-measures and dimension theory
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by D. J. Grubb PDF

Proc. Amer. Math. Soc. 128 (2000), 1105-1108 Request permission

Abstract:

A quasi-linear functional on $C(X)$ is a real-valued function that is linear on each closed, singly generated subalgebra and is norm bounded. We show that if the covering dimension $\dim X\leq 1$, then every quasi-linear functional on $C(X)$ is, in fact, linear. We do this by considering an associated set function, called a quasi-measure, and ask when such a set function can be extended to be a measure.

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