Condition on when we can do Riemann-Stieltjes Integral

Condition on when we can do Riemann-Stieltjes Integral

0:00 start
0:27 prove f is integrable if and only if upper sum - lower sum can be arbitrary small

11:58 prove a function is continuous then the function is Riemann-Stieltjes Integrable
17:16 prove a function is monotone and if alpha is continuous then function is Riemann-Stieltjes Integrable

20:45 a function is riemann integrable if there is finite discontinuous point but at that point,
alpha is continuous

28:45 continuous function composite with the integrable function is continuous

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