Lets say we have the following sets: (a) set consisting of a single point (b) set consisting of finite number of points in a plane (c) union of a finite collection of line segments in a plane. We want to prove that each of these sets is measurable and has zero area. Ok so here is how I started:(adsbygoogle = window.adsbygoogle || []).push({});

So for (a) Q is a step that can be enclosed between two step regions S and T so that there is one c which satisfies the inequalities [tex] a(S) \leq c \leq a(T) [/tex] for all regions S and T satisfying this then Q is measurable and [tex] a(q) = c [/tex] So should I choose c = 0? This will be both less than and greater than two given areas. Should I do the same thing for the other parts?

Thanks a lot

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Measurable Sets

**Physics Forums | Science Articles, Homework Help, Discussion**