Do physicists know the Lebesgue integral?

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Discussion Overview

The discussion revolves around the relevance and necessity of the Lebesgue integral in the field of physics, particularly whether physicists are taught it and how it applies to their work. The scope includes theoretical considerations, educational aspects, and practical applications in physics.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question whether physicists generally require the Lebesgue integral and if it is part of their graduate education.
  • One participant suggests that while Lebesgue measure is useful in probability theory, its application in physics may vary.
  • A distinction is made between different types of physicists: mathematical physicists are said to need the Lebesgue integral for understanding proofs in functional analysis, while theoretical physicists may find it necessary, and experimental physicists may not use it at all.
  • Another participant posits that the necessity of the Lebesgue integral depends on the complexity of the entities being integrated, suggesting that simpler physical shapes might be adequately handled by Riemann integration.
  • A participant expresses skepticism about the qualifications of others to discuss physicists' needs regarding the Lebesgue integral, given their stated lack of knowledge in physics.
  • A mathematician asserts that while Lebesgue integration is essential for proving theorems related to integrals, its practical applications in physics may depend on understanding the limitations of the theory.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and application of the Lebesgue integral among physicists, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

There are limitations regarding the assumptions made about the types of integrals physicists encounter and the definitions of necessity in their work. The discussion does not resolve the varying educational backgrounds and practical needs across different branches of physics.

imurme8
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Do physicists in general have need of the Lebesgue integral? Are they taught it in graduate school?
 
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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.
 
Mathematical physicists: Yes.
Theoretical physicists: Maybe.
Experimental physicists: No.

Mathematical physicists need it mainly to understand proofs in books on functional analysis.
 
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.
 
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:
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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