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Riemann Stieltjes Integration

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

&#946;(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 &#946; if and only if f is continuous at x=0.


Solution Summary

Riemann-Stieltjes integration is investigated.