Measurable Subset Question

1)Let be a measurable subset of with and let be a sequence of measurable subsets of . If, for any , there exists a set in the sequence with , find the value of .

My working is as below:

Since & ,

, so .

So set such that for

So .

Hence .

Is this correct?

2)Let be a measurable set with . Suppose that is a sequence of measurable subsets of such that for . Find .

I suppose the answer is 1?

Re: Measurable Subset Question

Quote:

Originally Posted by

**Markeur** 2)Let

be a measurable set with

. Suppose that

is a sequence of measurable subsets of

such that

for

. Find

.

I suppose the answer is 1?

Yes, because each of the complementary sets is a null set, and the union of countably many null sets is null.