The theory of stochastic integration relies on the concept of the Lebesgue-Stieltjes integral. However, it is hard to find a textbook that handles this concept in detail.
Take, for instance, Chung and Williams' textbook "Introduction to Stochastic Integration", 2nd edition (Birkhaeuser 2014). Section 1.3, titled "Functions of Bounded Variation and Stieltjes Integrals", lists facts, but does not prove them nor gives reference for further reading.
Where can I turn to (a textbook, online class notes, etc.) to fill in the gaps and read an orderly exposition of the subject matter that accounts for all the results pertinent to stochastic integration, and, in particular, those cited in Chung and Williams' section 1.3?
P.S. The reference need not be in English.