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Homework Help: Another regulated functions question

  1. Jan 21, 2010 #1

    C.E

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    1. suppose f:[a,b]->R is a weakly increasing function, i.e. u<v gives f(u)<=f(v). Show that f is the limit of a sequence of step functions.

    3. I have no idea how to start this. Please help.
     
  2. jcsd
  3. Jan 21, 2010 #2
    If you were to draw the graph of [tex]f[/tex] on a computer monitor, what would the picture look like?

    Now buy successively better computer monitors :)
     
    Last edited: Jan 21, 2010
  4. Jan 22, 2010 #3

    C.E

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    Surely different choices of f would look different wouldn't they? How do this help?
     
  5. Jan 22, 2010 #4
    Of course the sequence of approximating step functions will depend on the particular function [tex]f[/tex]. My hint is that you should approximate the graph of [tex]f[/tex] roughly as a computer monitor does.
     
  6. Jan 22, 2010 #5

    C.E

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    Sorry, but I don't know how a computer monitor would aproximate the graph of f, can you please elaborate?
     
  7. Jan 22, 2010 #6
    Think of square pixels -- approximate the graph of [tex]f[/tex] by something you might draw using the edges of a square grid.
     
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