given $(X,\mathcal{M})$ a measurable space, I Have $E \subset X$ and $\chi_{E}$ is an indicator function. then what is meant by $f_{\chi_{E}}$ ?
I am not very clear with this notation and meaning.
2026-04-28 13:49:50.1777384190
meaning of $f_{\chi_{E}}$
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The short answer: it's probably the function $f$ restricted to the set $E$. That is, it's probably the product $f\chi_E$.
The long answer: it's whatever your author wanted it to mean. The absolute source here is the book/lecture notes/person who presented the notation, as relatively little notation in math is truly standardized.