Necessary and Sufficient Condition for the Quaternion Vector Measure

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.

Authors:

• Mei Li
• Fahui Zhai

Keywords:

• Quaternion
• Quaternion measure
• Quaternion vector measure
• Quaternion Banach space
• Quaternion linear functional.

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