# Questions tagged [almost-everywhere]

For questions about the concept of "almost everywhere", that is, questions about properties which holds everywhere, except on a set of measure 0. This is involved in probability theory as well as in the case of infinite measure space. Use the appropriate tags to specify the context.

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### Is the following characterisation of measurable functions true?

I am self studying measure theory.I measure theory it is often important to check if a function is measurable.If the function is continuous then it is measurable of course.But if the function is not ...
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### L2 convergence for a simple function approximation

Consider the problem on the picture. I am struggling with part (b) of the excercise. I have managed to show that we have $L^1$ convergence, but I am unable to show $L^2$ convergence. Does anyone have ...
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### A.e. $L^p$ convergence implies a.e. convergence along sub-sequence

The book on Bochner spaces that I am currently looking at contains the following theorem: Let $\tilde{u}:[0,T] \to L^p(a,b)$ be Bochner measurable for some $1\leq p< \infty$. Define u: [0,T] \...
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