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Assume $f$ and $g$ are two piecewise continuous functions on an interval $( a , b )$ containing the point $t_0$ . Assume further that $f$ has a jump discontinuity at $t_0$ while $g$ is continuous at $t_0$ .How can i verify that the jump in the product $fg$ at $t_0$ is given by “the jump in $f$ at $t_0$ ” × $g ( t_0 )$ ?

salv.t
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1 Answers1

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You can take the the two one-sided limits of $fg$, getting $\displaystyle \lim_{x \to t_0^+} f(x)g(x) - \displaystyle \lim_{x \to t_0^-} f(x)g(x)$.

Ross Millikan
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