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Additivity and linearity lemmas for Riemann and Riemann–Stieltjes integrals
A map of the linearity and interval-additivity rules for Riemann and Riemann–Stieltjes integrals
Core idea
This knowl is a navigation page for four independently reusable facts:
- Linearity of the Riemann integral
- Additivity of the Riemann integral over subintervals
- Linearity of the Riemann–Stieltjes integral
- Additivity of the Riemann–Stieltjes integral over subintervals
Together these rules make integration behave like a linear functional and permit interval decomposition.