- #1
kfdleb
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Homework Statement
f is of bounded variation on [a;b] if there exist a number K such that
[tex]\sum[/tex][tex]^{n}_{k=1}[/tex]|f(ak)-f(ak-1)| [tex]\leq[/tex]K
a=a_0<a_1<...<a_n=b; the smallest K is the total variation of f
I need to prove that
1) if f is of bounded variation on [a;b] then it is bounded on [a;b]
2) if f is of bounded variation on [a;b], then it is integrable on [a;b]
2. The attempt at a solution
i thought of using triangle inequation such that
0<=|f(b)-f(a)|<=[tex]\sum[/tex][tex]^{n}_{k=1}[/tex]|f(ak)-f(ak-1)| [tex]\leq[/tex]K
but I am not really sure how to prove the two statements
any help is really appreciated
thanks