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Extension of a theorem of Bochner on expressing functionals as Riemann integrals

1945
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Bulletin of the American Mathematical Society
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Introduction. S. Bochner 1 has shown that an additive homogeneous functional defined over a sufficiently large class C of functions can be realized as a Riemann integral with respect to a finitely additive measure V in the space X over which the functions are defined. His proof makes use of the fact that the constant function belongs to C, as a result, V(X) is finite. It is the purpose of this note to show that a similar theorem holds even when V(X) turns out to be infinite. A modification of

doi:10.1090/s0002-9904-1945-08323-2
fatcat:e27nclgtq5fkdp2j2kvxbcvqsm