- #1
nightingale123
- 25
- 2
Hello I have a question regarding something we wrote in class today.
Let ##A## be a bounded subset of ##R^n##, let ##f,g:A\to \mathbb{R}## be integrable functions on A.
##a)## if ## A## has a volume and ##\forall x \in A :m\leq f(x) \leq M## then ##mV(A)\leq \int_{A}f(x)\leq MV(A)##
this kinda surprised because I've always that that we could only integrate on sets who have a volume (circles squares etc.).
Could somebody give me an example of a set ##A## which does not have volume and a function ##f:A\to \mathbb{R}## which is integradable
Let ##A## be a bounded subset of ##R^n##, let ##f,g:A\to \mathbb{R}## be integrable functions on A.
##a)## if ## A## has a volume and ##\forall x \in A :m\leq f(x) \leq M## then ##mV(A)\leq \int_{A}f(x)\leq MV(A)##
this kinda surprised because I've always that that we could only integrate on sets who have a volume (circles squares etc.).
Could somebody give me an example of a set ##A## which does not have volume and a function ##f:A\to \mathbb{R}## which is integradable
Last edited: