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Do physicists know the Lebesgue integral?

  1. Jan 9, 2012 #1
    Do physicists in general have need of the Lebesgue integral? Are they taught it in graduate school?
  2. jcsd
  3. Jan 9, 2012 #2
    I'm not a physicist so I don't know. I'm told that Lebesgue measure is very useful for probability theory so I'm sure there's lots of times when it will be very useful for physics.
  4. Jan 11, 2012 #3


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    Mathematical physicists: Yes.
    Theoretical physicists: Maybe.
    Experimental physicists: No.

    Mathematical physicists need it mainly to understand proofs in books on functional analysis.
  5. Jan 11, 2012 #4
    As a disclaimer, I don't know anything about physics. However, I would guess that it would depend on the nature of things you will have to integrate. Many physical things, objects and natural-enough shape-esque objects will be sufficiently integrated with Riemann integration, but if you have to integrate more complicated entities, you will need the Lebesgue integral.
  6. Jan 11, 2012 #5


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    To gaussmouse and wisvuze: impressive that you both feel qualified to answer a question about physicists when you both claim you know nothing about physics.
    Last edited: Jan 11, 2012
  7. Jan 11, 2012 #6


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    As a mathematician I will say that Lebesgue integration is needed to prove theorems concerning integrals and related material. For applications it is only necessary to know what limitations the theory may impose.
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