LaTeX at this site.
Then repair this post so it is readable.
1. The problem statement, all variables and given/known data
f is of bounded variation on [a;b] if there exist a number K such that
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)|<= |f(ak)-f(ak-1)| K
but im not really sure how to prove the two statements
any help is really appreciated
Then to prove that is of bounded variation is simple since. We have that that and since is of bounded variation we have that . From where it follows that , thus it is bounded.
What do you have for the second one? Let me know.