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Riemann Stieltjes Integration

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Define the following functions on the closed interval [-1, 1]:

β(x) = { 0, for x<0
½, for x=0
1, for x>0

Let f:[-1,1]&#61664; R such that f is bounded.

Show that f is Riemann Stieltjes integrable with respect to β if and only if f is continuous at x=0.

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Riemann-Stieltjes integration is investigated. The functions on the closed interval is determined.

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Define the following functions on the closed interval [-1, 1]:

β(x) = { 0, for x<0
½, for x=0
...

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