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Reversal of the order of limits

  1. Jul 12, 2009 #1
    When is the aforementioned reversal valid? (For example, is continuity in the neighborhood of the limit sufficient?)

    Also, how would one prove this? In the example that I am analysing (that of the calculation of a second partial derivative), the function has a removable discontinuity at the point of the limit and also along both lines leading to it if the limits are taken indepedantly (one then the other).

    As I write thoughts of a possible proof form in my mind but any input would be much appreciated.
  2. jcsd
  3. Jul 13, 2009 #2


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    Science Advisor

    Generally speaking, if the convergence is uniform, you can swap limits. Actually, when it is possible to interchange limits is one of the major questions of Mathematical Analysis.
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