##  [Bounded Variation](/bounded-variation) 

  ##  [Bounded Variation](https://puremath.quantumdictionary.io/bounded-variation-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A real-valued function on an interval has bounded variation if the supremum, over all finite partitions of the interval, of the sum of absolute successive differences is finite; equivalently it can be written as the difference of two monotone increasing functions (Jordan decomposition).