I know that every absolutely continuous functions are of bounded(finite) variations but converse need not be true. and the cantor function is wellknown example of function of bounded variation which is not absolutely continuous. I want to know some other examples. Please help me! Thanks in advance!
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closed as off topic by George Lowther, Bill Johnson, Emil Jeřábek, Willie Wong, S. Carnahan♦ Jun 22 '12 at 15:48Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 


A real valued function $f:[a,b]\rightarrow \mathbb {R} $ is of bounded variation iff it is the difference of two bounded monotonically increasing functions. This gives you many  in fact all real real valued  examples. (See, eg., Rudins 'Real and Complex Analyis', Exercise 7.13) 

