Show that if A is measurable set then the set 3A : = { 3a : a Є A} is measurable. Find its measure. How about the set -3A? Give proofs to your answers. [20 marks]

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- August 22nd 2008, 02:34 PMcynthiacheokreal analysis...pls help me prove this!
Show that if A is measurable set then the set 3A : = { 3a : a Є A} is measurable. Find its measure. How about the set -3A? Give proofs to your answers. [20 marks]

- August 22nd 2008, 02:44 PMThePerfectHacker
I am not sure how you are defining "measurable", I will assume you mean Jordan measurable.

Also where is a subset of? It will be assumed that .

Let show that and conversely.

Let .

Since is measurable it means can be covered by intervals so that .

If define .

Then cover and .

Thus, is measurable. - August 25th 2008, 03:00 AMcynthiacheok
thanks,but wat about the measure of it?The measure we are talking about here is lebesgue measure

- August 25th 2008, 09:37 AMmathgeek777