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Thread: proof

  1. #1


    Let x1, x2,... be an enumeration of the jump points. Show that each jump is associated with a subinterval of [f(a), f(b)]. What are the endpoints of the ith jump subinterval.
    Show all jump subintervals are either disjoint or at most share an endpoint.

    Let [a1, b1], [a2, b2], ...[an, bn]be the first n jump intervals. We may relabel them so that a1<b1<a2<b2< So the sum of the lengths of the first n – subintervals is (b1-a1)+(b2-a2)+...+(bn-an)<=(a2-a1)+(a3-a2)+...+(f(b)-an)
    finish the proof from here.
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  2. #2
    Global Moderator

    Nov 2005
    New York City
    Can you give an example of just you are doing?
    Suppose for example,
    \tan x its jump points can be enumerated. Now what?
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