where P={x0,,xn}image is a partition of [a,b]image.

Example 10.23

Given fixed fC(a,b)image, the function

F(u)=abf(x)du(x),uBV(a,b) (10.7)

image (10.7)

is a continuous linear functional on BV(a,b). The linearity follows from Theorem 10.4(b), and the continuity ...

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