Is there a name for the relation $\int^b_a f(x)\ dx=\int_a^c f(x)\ dx+\int_c^b f(x)\ dx$?

Asked May 07 '15 at 09:03

Active May 07 '15 at 09:05

Viewed 59 times

The question is contained in its title. French mathematicians would call such a relationship "Chasles' relationship". This comes for the similarity with the formula $\vec{AB}=\vec{AC}+\vec{CB}$ for vectors that is also called "Chasles' relationship".

Is there a similar name in English?

edited May 07 '15 at 09:05

asked May 07 '15 at 09:03

Taladris

11,339
5
32
58

I have heard this called interval decomposition, but I do not know if that is the official name for this property. – May 07 '15 at 09:05
I think it is the same name which is used : Chasles' relation. – Claude Leibovici May 07 '15 at 09:08
I would call it additivity, since it generalizes to the additivity of the signed measure $E \mapsto \int_E f(x) , dx$ with integrable $f$ (though this covers only the case $a\leq c\leq b$). But many preliminary analysis textbooks just seem to leave it unnamed. – Sangchul Lee May 07 '15 at 10:11

Is there a name for the relation $\int^b_a f(x)\ dx=\int_a^c f(x)\ dx+\int_c^b f(x)\ dx$?

0 Answers0