Let f be a bounded function on [a, b] and P a partition of [a, b]....
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Let f be a bounded function on [a, b] and P a partition of [a, b]. If P* is any refinement of P, then (i) U(P*, ƒ)<U(P, ƒ), (ii) L(P*,ƒ)>L(P,ƒ). Let f be a bounded function on [a, b] and P a partition of [a, b]. If P* is any refinement of P, then (i) U(P*, ƒ)<U(P, ƒ), (ii) L(P*,ƒ)>L(P,ƒ).
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