Continuous mapping theorem counterexample

Asked Mar 13 '16 at 15:16

Active Mar 13 '16 at 15:16

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let g be a continuous function. Then from the continuous mapping theorem We have the following result. If xt converges to x* wp1 as t goes to infinity then g(xt) converges to g(x*) wp1

Now suppose g is only piecewise continuous. Do we have an example Which demonstrates the conclusion Of the continuous mapping theorem Does not hold when g is not continuous?

asked Mar 13 '16 at 15:16

RMG

Welcome to Math.SE. This site uses MathJax formatting – JKnecht Mar 13 '16 at 15:18
Think an example such that $g$ is discontinuous at $x^*$ with positive probability... – user251257 Mar 13 '16 at 16:04
Thanks! That was very helpful! – RMG Mar 14 '16 at 02:36

Continuous mapping theorem counterexample

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