L~tP := {(Ij' Ij)}7=. be a tagged partition of [a, b] and let c. < c2.(a)

Chapter 7, Problem 5

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L~tP := {(Ij' Ij)}7=. be a tagged partition of [a, b] and let c. < c2.(a) liub~toasubintervalIj whosetagsatisfiesc( ~ tj ~ c2,showthatcl -liP II~ u ~c2+IIPIi. ~(b) If v E [lr, b] and satisfies c( + IIPII ~ v ~ c2 - liP II,then the tag Ij of any subinterval Ijthat contains v satisfies tj E [c.' c2].

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