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Results tagged with measure-theory
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user 19603
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
1
vote
Accepted
What does it mean to say "almost always" ?
I see some contradiction in your hypotheses: since the $A_j$'s are disjoint and have non empty interiors, the union should be at most countable (there can't exist more $A_j$'s than the cardinal of the …
10
votes
Accepted
Lebesgue measure of some set of irrational numbers
The continued fraction expansion is related to the Gauss transformation $T:(0,1)\to(0,1)$, defined by
$$ Tx:=\frac{1}{x} \mod 1. $$
(Indeed, if $x=[a_1,a_2,\ldots)$, then $Tx=[a_2,a_3,\ldots)$.)
It i …