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Mathematical Analysis Fundamentals by Agamirza Bashirov

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image (9.10)

This function has the following properties.

Theorem 9.25

If fR(a,b)image, then FC(a,b)BV(a,b)image, where Fimage is defined by Eq. (9.10) .

Proof

Let ax<ybimage. Then

F(y)-F(x)=xyf(t)dtxyf(t)dtfB(y-x),

proving that FC(a,b). If P={x0,,xn}

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