Talk:Bounded variation

message: The "Algebraic Operations with BV Functions" section was removed since it violated the WP:COI policy and also it was a (fortunately short) mere collection of trivial facts. First of all, the space of BV functions is a vector space and the proof (for the one variable case) is very simple and compactly presented in standard texts as , therefore it is closed under subtraction and addition. It is an algebra as already stated in the related section of the article, therefore it is also closed under multiplication. The quotient of two functions of such space could not belong to the same space, as the following trivial example shows: consider the two functions 1 ∈ BV([-1,1]) and x ∈ BV([-1,1]). Then 1/x ∉ L1([-1,1]), i.e. the quotient of such functions of bounded variation is not even integrable on the [-1,1] interval. Similar elementary examples also show that closure under composition is trivially false: further, the composition of two function belongs to the realm of analytic operations therefore, strictly speaking, it is not an algebraic operation (even if can be studied using the methods of abstract algebra). Daniele.tampieri (talk) 16:21, 31 October 2011 (UTC)
thread_title:  About the removig of the "Algebraic Operations with BV Functions" section 

message: The sentence from the article:
One of the most important aspects of functions of bounded variation is that they form an algebra of discontinuous functions whose first derivative 
doesn't say what is meant. At least it is logically inconsistent, as continuous functions are of bounded variation. 82.75.140.46 (talk) 09:58, 26 January 2012 (UTC)
thread_title:  Algebra 

message: The notation used in this article is ugly and overcomplicated. Even the very first definition about bounded variation for a 1-variable function is notated in an overly complicated manner.  Similarly with the left and right limits being notated as x_{0^-} and x_{0^+} instead of x^-_0 and x^+_0. What a confusing article. 00:00, 27 January 2012 (UTC)
thread_title:  Simplify 

message: BV function with a removable discontinuity:
http://www.encyclopediaofmath.org/index.php/Function_of_bounded_variation#Continuity
(Warning 6)  — Preceding unsigned comment added by 132.230.12.59 (talk) 11:44, 11 June 2013 (UTC)
thread_title:  "BV functions have only jump-type discontinuities" 

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thread_title:  External links modified 

message: The single-variable case assumes continuity of f. This seems unnecessary and is not done in Wolfram MathWorld's article on BV. And it makes the first property proven (only jump-type and removable discontinuities) trivial. Why was continuity assumed? It appears to be safe to remove it.  — Preceding unsigned comment added by 69.253.18.244 (talk) 18:10, 1 June 2020 (UTC)
replies: text: In fact the only point where continuity was implicitly assumed was the chain of inclusions in the introduction.  This chain of inclusions is not very relevant and it is repeated in several other articles, and it could even be removed; I've added "continuous".pma 22:43, 2 November 2020 (UTC)
thread_title:  Continuity assumption? 

message: The examples start off with two cases which aren't bounded variations. I'm not sure whether that's the best way to present examples. Isn't it better to first show what are bounded variations, before introducing things which aren't? 62.216.5.216 (talk) 19:51, 2 November 2020 (UTC)
replies: text: That's true, but a large class of examples is already mentioned in the inclusions in the introduction. Maybe this could be recalled in the section of examples pma 22:50, 2 November 2020 (UTC)
thread_title:  Examples