Rotwang
Posts:
1,685
From:
Swansea
Registered:
7/26/06


Lebesgue measure on an uncountable product of intervals
Posted:
Apr 25, 2013 12:57 PM


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)?

