Re: complete measure

From: Daniel Grubb (grubb_at_lola.math.niu.edu)
Date: 09/23/04 

Date: 23 Sep 2004 14:22:47 GMT

>Please help me with this problem:

>Let m* is a outer measure on a set W, A* system of of all m*-measurable
>sets A in W, m*|A* - restriction of m* to A*.

>I have to prove that

>1) m*|A* is complete.

>2)If A is a sigma algebra in a set W, w in W and {w} in A, then the Dirac
>measure e_w on A is complete just when A=P(W) (P(W)-power set).

>A measure m on a sigma-algebra A in W is called complete if every subset
> of a m-null set belongs to A, and consequently is itself a m-null set.
>Thank you.

Help: 1) Look up the definition of m*-measurable. Now show that
any subset of a m*-null set is m*-measurable.

2) Look up the definition of the Dirac measure.

Additional help: Do your own homework. Especially when it is trivial.

--Dan Grubb