Mixing
Is exceptional set countable or uncountable?
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In Pollicott and Simon paper https://www.jstor.org/stable/2154881?seq=4#metadata_info_tab_contents Corollaty 1 gives cardinality of set of discontinuity points (exceptional set) is $ aleph $.
And in section 4 (comments and open questions), (2) he wrote that he do not know that exceptional set is countable or uncountable.
but i think $ frac{ln{l}}{-ln{lambda}} $ is increasing for $ lambda in [1/n,1/l] $ and we know that for monotone function on bounded closed internal has at most countably many discontinuity points.
So i think exceptional set must be at most countable.
real-analysis discontinuous-functions
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
$endgroup$
add a comment |
$begingroup$
In Pollicott and Simon paper https://www.jstor.org/stable/2154881?seq=4#metadata_info_tab_contents Corollaty 1 gives cardinality of set of discontinuity points (exceptional set) is $ aleph $.
And in section 4 (comments and open questions), (2) he wrote that he do not know that exceptional set is countable or uncountable.
but i think $ frac{ln{l}}{-ln{lambda}} $ is increasing for $ lambda in [1/n,1/l] $ and we know that for monotone function on bounded closed internal has at most countably many discontinuity points.
So i think exceptional set must be at most countable.
real-analysis discontinuous-functions
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
$endgroup$
add a comment |
$begingroup$
In Pollicott and Simon paper https://www.jstor.org/stable/2154881?seq=4#metadata_info_tab_contents Corollaty 1 gives cardinality of set of discontinuity points (exceptional set) is $ aleph $.
And in section 4 (comments and open questions), (2) he wrote that he do not know that exceptional set is countable or uncountable.
but i think $ frac{ln{l}}{-ln{lambda}} $ is increasing for $ lambda in [1/n,1/l] $ and we know that for monotone function on bounded closed internal has at most countably many discontinuity points.
So i think exceptional set must be at most countable.
real-analysis discontinuous-functions
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
$endgroup$
In Pollicott and Simon paper https://www.jstor.org/stable/2154881?seq=4#metadata_info_tab_contents Corollaty 1 gives cardinality of set of discontinuity points (exceptional set) is $ aleph $.
And in section 4 (comments and open questions), (2) he wrote that he do not know that exceptional set is countable or uncountable.
but i think $ frac{ln{l}}{-ln{lambda}} $ is increasing for $ lambda in [1/n,1/l] $ and we know that for monotone function on bounded closed internal has at most countably many discontinuity points.
So i think exceptional set must be at most countable.
real-analysis discontinuous-functions
real-analysis discontinuous-functions
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
asked Jan 6 at 13:48
Uswadkar Prashant VasantraoUswadkar Prashant Vasantrao
506
506
add a comment |
add a comment |
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