I'm working on my understanding of measurable sets and my immediate intuition wants to know what's not a measurable set? Initially I think of some space where divisions go to infinity, like a tolerance that just is defined to go on and on. For example plus or minus infinity from a to b would be unmeasurable. Does that even make sense? Furthermore measurable sets are topologies, which seemingly implies a very important property, because then one can find a defined function between any two measurable sets. In the end my biggest question is what's not a measurable set? Note: I'm learning measurability from the point of view a Lebesgue integral.
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Lebesgue measure is made this way. It should contain all "inuitively alright" sets. – Daniel Valenzuela Sep 22 '14 at 08:08
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Is that a Lebesgue quote? – vajra78 Sep 22 '14 at 08:16
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Actually I think there is no example of a non-measurable set -- we may only prove the existence of such sets. See Non-Borel set. Also see Vitali set. – Florian Sep 22 '14 at 08:25
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1And Examples of non-measurable sets – Florian Sep 22 '14 at 08:28
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No it is not a quote. But it is motivation. – Daniel Valenzuela Sep 22 '14 at 08:28
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Ok so a non-measurable is almost artistically abstract in a sexy pure mathematical way – vajra78 Sep 22 '14 at 08:37
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Basically you"ll never run across a non measurable signal? Even uncertainty implies measurability but it's just uncertain. – vajra78 Sep 22 '14 at 08:46