List questions from lebesgue-integral

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Generalizability of a measure

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Defining an Antiderivative for Monotone Functions

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Is there a way to make sense of an integral over an interval deprived of an infinite number of values?

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folland Exercise 2.24

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Find a sequence $\left\{f_{n}\right\}$ of Borel measurable functions on $\mathbb{R}$ which...

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showing $\int_\mathbb{R}g(t) d\nu(t) = \int_\mathbb{R}g(f(s))d\mu(s)$ for $g$ a measurable simple function

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proving big-omega with an integral (problem with bringing supremum of function outside of the integral sign)

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Inequality with convex function and conditional expectation

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In regard to $L^p$ spaces, is $L^p \subset L^q$ for $p<q$?

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Show that $\lim_{p\to\infty}\int_{A}f^{p}d\mu=\infty$.

Published on 14 Jan 2020 - 3:03

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Dominated convergence theorem on a subset $A\subseteq\mathbb{R}^n$, where the dominating function is not integrable on $\mathbb{R}^n$.

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Is $\frac{\sin(x)}{x}$ Lebesgue-Integrable?

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Dominated convergence theorem counterexample

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contradiction to Fubini's theorem

Published on 27 Mar 2026 - 14:59

List Question

Integrability proof

Generalizability of a measure

Defining an Antiderivative for Monotone Functions

Is there a way to make sense of an integral over an interval deprived of an infinite number of values?

folland Exercise 2.24

Find a sequence $\left\{f_{n}\right\}$ of Borel measurable functions on $\mathbb{R}$ which...

showing $\int_\mathbb{R}g(t) d\nu(t) = \int_\mathbb{R}g(f(s))d\mu(s)$ for $g$ a measurable simple function

proving big-omega with an integral (problem with bringing supremum of function outside of the integral sign)

Inequality with convex function and conditional expectation

In regard to $L^p$ spaces, is $L^p \subset L^q$ for $p<q$?

Show that $\lim_{p\to\infty}\int_{A}f^{p}d\mu=\infty$.

Dominated convergence theorem on a subset $A\subseteq\mathbb{R}^n$, where the dominating function is not integrable on $\mathbb{R}^n$.

Is $\frac{\sin(x)}{x}$ Lebesgue-Integrable?

Dominated convergence theorem counterexample

contradiction to Fubini's theorem

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