To keep the lecture self-contained, we provide here references or even proofs to some results not proven in the class.
This material is not obligatory (will not be required for exams).

Bochner integral: short treatment can be found in [1]; more comprehensive exposition is here.

Absolutely continuous (scalar) functions, Lebesgue differentiation theorem: see [1] or [2].

Direct proof of Theorem 1.9 -- on dual space to L^p(I;X) -- is here.

Continuity of Niemycki operators here (in czech only).

[1] Lukeš, Malý: Measure and integral.
[2] Rudin: Real and complex analysis.