Im looking at the proof of the Lebesgue differentiation theorem on wikipedia: https://en.wikipedia.org/wiki/Lebesgue_differentiation_theorem#Proof
I don't see why this line is true.
This looks like the triangle inequality but it's an equality?
2026-03-30 15:11:47.1774883507
The proof for the Lebesgue differentiation theorem
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Just look at the terms on the right side. The terms $-\frac 1 {|B|} \int_B g(y)dy$ and $+\frac 1 {|B|} \int_B g(y)dy$ cancel each other and so do the terms $-g(x)$ and $+g(x)$.