Discussion Overview
The discussion revolves around the measurability of integrals in the context of Tonelli/Fubini's Theorem, specifically examining the implications of different notational forms when expressing measurability.
Discussion Character
Main Points Raised
- One participant questions the difference between stating that the function \( y \mapsto \int_E f^y(x) dx \) is measurable and stating that \( \int_E f^y(x) dx \) is measurable.
- Another participant argues that there is no significant difference, suggesting that the first statement emphasizes the integral as a measurable function of \( y \).
- A third participant describes the second statement as a less formal version of the first, comparing it to saying that \( x^2 \) is differentiable instead of stating that \( x \mapsto x^2 \) is differentiable.
Areas of Agreement / Disagreement
Participants appear to agree that the two statements convey similar meanings, though they express differing views on the formality and emphasis of the notation used.
Contextual Notes
The discussion does not resolve any deeper implications of measurability or the broader context of Tonelli/Fubini's Theorem.