Lecture 6: The Double Dual and the Outer Measure of a Subset of Real Numbers

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Brian G. Valentine +2
Brian G. Valentine

The norm is a real valued function, the range of the bounded linear functionals is the field of complex numbers. In your demonstration of boundedness, you are comparing the size of a real number to a complex number, which doesn't make sense. You need the magnitude of the complex number in front of the norm.

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