Re: A question in real analysis!

On 12 Apr 2007 23:53:03 -0700, "Gary Cooper" <ghkrhdwk@xxxxxxxxxxx>
wrote:

On 4¿ù12ÀÏ, ¿ÀÈÄ2½Ã39ºÐ, The World Wide Wade <aderamey.a...@xxxxxxxxxxx>
wrote:
In article <1176345719.743393.79...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Gary Cooper" <ghkrh...@xxxxxxxxxxx> wrote:

Hi.

In exercising the Rudin's RCA problem, this problem pushed me into
despair.

'Show that every compact subset of R is the support of a borel set.'

Can you help me?

Assuming you mean the support of a Borel measure, here's a hint: every
compact metric space has a countable dense subset.

I think you means that construct a linear functional using your hint.
And apply Riesz representation theorem to get a positive measure which
is desired.

Interesting theory. _I_ tend to think that he meant exactly
what he said.

Given a single point x, can you think of a measure that
has support equal to {x}?

But how to construct that functional using your hint?


************************

David C. Ullrich
.

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