# Homework Help: Measurable Sets

1. May 13, 2005

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:

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 $$a(S) \leq c \leq a(T)$$ for all regions S and T satisfying this then Q is measurable and $$a(q) = c$$ 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

2. May 14, 2005