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accepted Is there a natural measurable structure on the $\sigma$-algebra of a measurable space?
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comment Is there a natural measurable structure on the $\sigma$-algebra of a measurable space?
Let no one say category theory lacks practical applications. Thanks for the tip & the existence theorem, David! I will be very interested to hear more about the natural $\sigma$-algebra on the space of measurable functions Hom($X$, $Y$). Can you add some more details to your answer as to what that $\sigma$-algebra looks like? e.g., what are examples of measurable sets of maps, and do those form a base for the $\sigma$-algebra? What do functorality & right-adjointness mean in this context?
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comment Example of a space for which $V \cong Hom(V,V)$
Also, can you demonstrate this property in your answer? I'll be happy to accept it in that case.