Properties of integration on Jordan Regions and stuff

[SNOOTCHIEBOOCHEE]

Homework Statement

Let f : Rn ----> R.
i) Let E1 and E2 be two Jordan regions in Rn such that E1 C E2 Suppose f is integrable
on E2. Then, show that f is integrable on E1.
ii) Suppose f is continuous on Rn. Then, show that f is integrable on any Jordan region
E in Rn. Here, E is bounded.

The Attempt at a Solution

These both seem really easy to me and i can't figure it out.


For part two, is it enough to show that E is of measure zero? and how do you do that?

 

[HallsofIvy]

How do you define integrable? Suppose f were NOT integrable on E1. What would that tell you about the integral on E2?

As for (ii), you are told only that E is bounded. Why in the world would you think that it has measure 0?