About Jordan volume

Asked Jun 01 '13 at 20:07

Active Jun 01 '13 at 20:26

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I have a multivariate calculus homework, and I don't understand completely the definition of Jordan volume. Here's my question:

Be $R \subset \mathbb{R}^2$ with Jordan area and for each $h>0$ be $C(R,h)\subset \mathbb{R}^3$ defined by:

$$C(R,h) := \lbrace (x,y,h) \in \mathbb{R}^3: (x,y)\in R\rbrace$$

Show that $C(R,h)$ have Jordan volume and calculate it.

If you could help me I would greatly appreciate.

edited Jun 01 '13 at 20:26

asked Jun 01 '13 at 20:07

El Peluca Sapeeee

1

In the definition of $C(R,h)$, presumably you want a condition on $z$ (something like $|z| \leq h$, perhaps)? – Stephen Jun 01 '13 at 20:10
@Steve Yes! sorry, I'll fix right now. – El Peluca Sapeeee Jun 01 '13 at 20:26
Oh, so it's a copy of the region $R$ lifted to height $h$, but now we have to consider the Jordan volume. For every way you have of covering $R$ by disjoint rectangles, you can cover $C(R,h)$ with corresponding boxes of some given height. This should get you started. – Ted Shifrin Jun 01 '13 at 20:29
@TedShifrin ok! I have the idea, I'll try to do it. Thanks. – El Peluca Sapeeee Jun 01 '13 at 20:56

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