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Topic: Lebesgue measure on an uncountable product of intervals
Replies: 4   Last Post: Apr 27, 2013 8:18 AM

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Rotwang

Posts: 1,679
From: Swansea
Registered: 7/26/06
Lebesgue measure on an uncountable product of intervals
Posted: Apr 25, 2013 12:57 PM
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Hi all,

I'm reading Yuri Manin's /A Course in Mathematical Logic for
Mathematicians/, and in a chapter on the continuum hypothesis he writes
this:

Let I be a set of cardinality > omega_1. We set

Omega = [0, 1]^I, with Lebesgue measure [...]

Here omega_1 is the first uncountable ordinal. My question is, how does
one define the Lebesgue measure on [0, 1]^I when I is infinite (and, in
particular, uncountable)?



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