6. The Riemann-Stieltjes integral

• $\mathscr{R}$,
  • set of all Rieman integral functions
• $\mathscr{R}(\alpha)$
  • set of all Rieman-Stieltjes integral functions
  • integrale with respect to $\alpha$, in the Riemann sense
  • $\alpha$ monotonoically increasing function