The Space of Complex Measures
The sum of two complex measures is a complex measure, as is the product of a complex measure by a complex number. That is to say, the set of all complex measures on a measure space (X, Σ) forms a vector space. Moreover, the total variation ||μ|| defined as
is a norm in respect to which the space of complex measures is a Banach space.
Read more about this topic: Complex Measure
Famous quotes containing the words space, complex and/or measures:
“But alas! I never could keep a promise. I do not blame myself for this weakness, because the fault must lie in my physical organization. It is likely that such a very liberal amount of space was given to the organ which enables me to make promises, that the organ which should enable me to keep them was crowded out. But I grieve not. I like no half-way things. I had rather have one faculty nobly developed than two faculties of mere ordinary capacity.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“All propaganda or popularization involves a putting of the complex into the simple, but such a move is instantly deconstructive. For if the complex can be put into the simple, then it cannot be as complex as it seemed in the first place; and if the simple can be an adequate medium of such complexity, then it cannot after all be as simple as all that.”
—Terry Eagleton (b. 1943)
“Away with the cant of “Measures, not men!”Mthe idle supposition that it is the harness and not the horses that draw the chariot along. No, Sir, if the comparison must be made, if the distinction must be taken, men are everything, measures comparatively nothing.”
—George Canning (1770–1827)