Timeline for When is the set of measurable functions a vector space?
Current License: CC BY-SA 4.0
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| Jan 4, 2021 at 13:43 | vote | accept | UserA | ||
| Jan 4, 2021 at 13:12 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Jan 4, 2021 at 12:54 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Jan 4, 2021 at 12:17 | comment | added | UserA | Thank you for the helpful answer. For clarificartion: - when $Y$ is a separable Banach space, are any assumptions needed on $X$ to show that $L^0(X,Y)$ (in the sense of Bochner measurable) is vector space ? - You said "or $X$ is a perfect measure space". In this case, does it suffice to take $Y$ as a topological vector space? - In any of two cases above, can you outline how we get the vector space structure on $L^0(X,Y)$? Also, it would be also be great if you can remember the counter example! | |
| Jan 4, 2021 at 12:00 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Jan 4, 2021 at 11:55 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
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| Jan 4, 2021 at 11:45 | history | answered | Gerald Edgar | CC BY-SA 4.0 |