In the Notes section of chapter 2 of Diestel and Uhl's Vector Measures they make the comment:

"Presently the Pettis integral has very few applications. But our prediction is that when (and if) the general Pettis integral is understood it will pay off in deep applications." ( Google books link )

That was back in $1977$ and when I did a little searching to find out how well that prediction had fared I found little: wikipedia provides a cursory description and Encyclopedia of Mathematics is arguably better but terser. This question asks why (Dunford-)Pettis integrals are useful, but I would not say it covers deep applications per se.

So: are there deep applications to the Pettis integral, and if so, what are they?


Diestel and Uhl commented on this in Measure theory and its applications:

enter image description here enter image description here

| cite | improve this answer | |
  • $\begingroup$ That's excellent, thank-you! $\endgroup$ – postmortes Jul 30 at 11:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.