I am having trouble understanding what the positive variation of a function $\frac{ 1}{2} ( T_F + F)$ represents. (Where, in this case, $T_F$ is the total variation of $F$ from $[0,x]$.) For consider $F = 1-x$ on $[0,1]$. In this case $T_F(x) = x$. Therefore The positive variation of this function is $\frac{ 1}{2} ( T_F + F) = \frac{ 1}{2} ( x + 1-x) = \frac{ 1}{2}$ on the entire interval $[0,1]$. What does this represent? (The notation I am using here comes from Folland's Real Analysis.)
2026-03-25 09:50:49.1774432249
What is the positive variation of a function?
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