Definition:Lp Space/Warning

$L^p$ Space: Warning
In most discussions of $L^p$ spaces, a mapping is not distinguished from the equivalence class it occupies.

That is, for $f \in \map {\LL^p} {X, \Sigma, \mu}$, no distinction is made between the objects $f$ and $\eqclass f {\sim_\mu}$.

On, we maintain the distinction for foundational results, but in advanced results it may be too cumbersome to do so, so this is not required for high-level results.

It should however always be noted where this lack of distinction may cause confusion, or is very important to the result.