Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: integral over difference of sets
Posted:
Nov 9, 2010 2:51 AM


On Nov 8, 8:17 pm, Arturo Magidin <magi...@member.ams.org> wrote: > On Nov 8, 12:37 pm, Anonymous wrote: > > > Hello everyone, > > I know that the integral of a simple function over the sum of two sets > > is the integral of the function over each individual set. (Additivity > > for simple functions). > > If both sets are measurable...
Redundant.
> > My question is if B is a subset of A. Is the > > integral over the difference (AB) the difference of the integrals, > > i.e the difference of the integtral of the function over A minus the > > integral of the function over B. > > > To put it another way does sum(ai* x m{x in AB > > yi1<=f(x)<yi})=sum(ai* x m{x in A yi1<=f(x)<yi}sum(ai* x m{x in > > B yi1<=f(x)<yi})? > > Since A = (AB)\/B, if both A and B are measurable, you can use the > first statement you say you know, apply it to (AB)\/B, and then > "solve" for the integral over AB.
Han de Bruijn



