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Necessary and Sufficient Condition for the Quaternion Vector Measure

Authors: Fahui Zhai, Mei Li


In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.

Keywords: quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional

Digital Object Identifier (DOI):

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