Question: Let (f) be continuous. Show that it does not affect the finiteness of (operatorname{VAR}_{p}(f ;[0, t])) and the numerical value of (operatorname{var}_{p}(f ;[0, t])) if

Let $f$ be continuous. Show that it does not affect the finiteness of $\operatorname{VAR}_{p}(f ;[0, t])$ and the numerical value of $\operatorname{var}_{p}(f ;[0, t])$ if we restrict ourselves to partitions not containing the endpoints 0 and $t$ of the interval. (In this case we have to define the mesh as mesh of $\Pi \cup\{0, t\}$ ).

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