Is it true that if $f\in L^1 (X,\mu)$ then $$\int_E |f| d\mu +\int_{E^c} |f| d\mu = \int_X |f| d\mu?$$
2026-04-21 22:24:28.1776810268
Measure Theory on integrals
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Note that $$\int_X|f|=\int_X\chi_E|f|+\int_X\chi_{E^c}|f|.$$