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
|f(a
_{k})-f(a
_{k-1})|
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)|<=
|f(a
_{k})-f(a
_{k-1})|
K
but im not really sure how to prove the two statements
any help is really appreciated
thanks