Does absolute continuity of a function $f:[a,b]\rightarrow E$ into some Banach space also ensures (i) measurability and (ii) differentiability almost everywhere, like it does on ${\bf R}$?
2026-04-09 09:08:14.1775725694
Absolute continuity in Banach spaces
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Of course they are measurable since they are continuous. I found a counterexample to differentiability though, but forgot the source, it was $$f:[0,1]\rightarrow L^1([0,1]):t\mapsto{\bf 1}_{[0,t]}$$