here is my question, show that the linear combination of two functions of bounded variation is also of bounded variation. Is the product of two such functions also of bounded variation?
Functions of bounded variation
2
$\begingroup$
real-analysis
-
2You don't have a better title for your question? – 2011-11-30
-
0I've provided a more informative title. – 2011-11-30
2 Answers
8
Hint: $f(x) g(x) - f(y) g(y) = f(x) (g(x) - g(y)) + (f(x) - f(y)) g(y)$.
3
Hint: For the first one, using the definitions show that the total variation of $f + g$ is at most the total variation of $f$ plus the total variation of $g$.