Abstract
As a consequence of a recent result due to Kaftal and Wiess it is shown that any vector measure (for the strong operator topology) with values in the space of compact operators on a Hilbert space is σ \sigma -additive for the uniform operator topology. This leads to an elegant and simple proof of a result due to Diestel and Faires on the uniform operator σ \sigma -additivity of the indefinite integral induced by a compact selfadjoint operator.
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