Show that on finite measure spaces, LP and almost everywhere convergence are independent. That is, for any p it is possible that a sequence of functions converges in LP but not a.e. and it is also...

Show that on finite measure spaces, LP and almost everywhere convergence are<br>independent. That is, for any p it is possible that a sequence of functions converges<br>in LP but not a.e. and it is also possible that it converges a.e. but not in LP.<br>

Extracted text: Show that on finite measure spaces, LP and almost everywhere convergence are independent. That is, for any p it is possible that a sequence of functions converges in LP but not a.e. and it is also possible that it converges a.e. but not in LP.

Jun 04, 2022

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Show that on finite measure spaces, LP and almost everywhere convergence are independent. That is, for any p it is possible that a sequence of functions converges in LP but not a.e. and it is also...

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