# Tagged Questions

Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.

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### Radon Nikodym Thm: extending to $\sigma$-finite case

I am reading Bartle's "Elements of Integration". Radon-Nikodym Thm: Let $\lambda,\mu$ be $\sigma$-finite measures on a measurable space $(X,\textbf{X})$ and say $\lambda \ll \mu$. Then $\exists$ ...
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### How can integrals be developed? [closed]

I wonder if it would be possible to develop integrals without any use of simple functions and "area approaches". Thank you.
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### Sets not in a sigma-algebra

I have a question concerning some sets which are not in a given sigma-algebra. More precisely, I have two questions closely related: Let $\mathcal{A}(\mathbb{R}_{\ge 0}, \mathbb{R}^d), d \ge 1$, be ...
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### Problem in measure theory. Which of the following are true? [closed]

Let $f : [a, b] \to \mathbb{R}$ be a measurable function. Then a) $\$ if $\int\limits_c^d f(x)dx = 0$ for all $a \leq c < d \leq b,$ then $f = 0$ a.e. b) $\$ if $\int\limits_a^c f(x)dx = 0$...
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### Baire measurable sets

I got the following setting: Let $X$ a uncountable set, $p \notin X$ and $X^* = X \cup \{p\}$. Let \mathcal O := \{O \subseteq X^* \mid O \subseteq X \text{ or } p \in O \text{ and } X \setminus O \...
Let $\mathcal{B}$ be the functions analytic on the unit disk and continuous on its boundary. With the supremum norm this becomes a Banach space. Is there any way to define a meaningful measure on ...