List questions from lebesgue-measure

Published on 05 Jul 2014 - 3:43

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Proof when the circle map is ergodic

Published on 27 Mar 2026 - 4:14

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Measures $\mu$ such that $\mu(a+A)\leq c\ \mu(A)$

Published on 06 Jul 2014 - 23:31

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Is it true that $f \in L_1([a,b])$ is the uniform limit of polynomials?

Published on 07 Jul 2014 - 15:50

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Prove that $f\in L^p[0,1]$ for all $p\in[1,2)$:

Published on 02 Apr 2026 - 18:42

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Functions with every point being a Lebesgue point

Published on 01 Apr 2026 - 6:29

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Help with Borel sets

Published on 09 Jul 2014 - 7:11

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For $E \subseteq [0, 1]$, $m(E) > 0$, show that there are $\alpha$ and $\beta$ such that $\alpha, \alpha + \beta, \alpha + 2\beta \in E$.

Published on 09 Jul 2014 - 16:10

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Finding a dominating function for this sequence of functions

Published on 27 Mar 2026 - 20:12

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Question on non-atomic measures

Published on 10 Jul 2014 - 17:11

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Show that $\int_X gdν=\int_X gfdμ$ for all $g∈L_1(ν).$

Published on 01 Apr 2026 - 8:05

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$\int_0^1f(x)dx = 2, \int_0^1g(x)dx = 1, \text{and} \int_0^1[f(x)]^2 dx ≤ C$ for some constant $C > 4.$

Published on 01 Apr 2026 - 8:06

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Why $\int f_0 \mbox{d}(F_0+F_1)=\int f_0 \mbox{d}F_0+\int f_0 \mbox{d} F_1=1$ should be true?

Published on 01 Apr 2026 - 8:06

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Show that $\lim_{a\to 0^+} \int \frac{e^{-|x|/a}}{2a}f(x)dx=f(0)$

Published on 16 Jul 2014 - 22:54

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Can we find uncountably many disjoint measurable subsets of $\mathbb{R}$ with strictly postive Lebesgue measure?

Published on 17 Jul 2014 - 3:25

List Question

Measure which does not grow faster than Lebesgue

Proof when the circle map is ergodic

Measures $\mu$ such that $\mu(a+A)\leq c\ \mu(A)$

Is it true that $f \in L_1([a,b])$ is the uniform limit of polynomials?

Prove that $f\in L^p[0,1]$ for all $p\in[1,2)$:

Functions with every point being a Lebesgue point

Help with Borel sets

For $E \subseteq [0, 1]$, $m(E) > 0$, show that there are $\alpha$ and $\beta$ such that $\alpha, \alpha + \beta, \alpha + 2\beta \in E$.

Finding a dominating function for this sequence of functions

Question on non-atomic measures

Show that $\int_X gdν=\int_X gfdμ$ for all $g∈L_1(ν).$

$\int_0^1f(x)dx = 2, \int_0^1g(x)dx = 1, \text{and} \int_0^1[f(x)]^2 dx ≤ C$ for some constant $C > 4.$

Why $\int f_0 \mbox{d}(F_0+F_1)=\int f_0 \mbox{d}F_0+\int f_0 \mbox{d} F_1=1$ should be true?

Show that $\lim_{a\to 0^+} \int \frac{e^{-|x|/a}}{2a}f(x)dx=f(0)$

Can we find uncountably many disjoint measurable subsets of $\mathbb{R}$ with strictly postive Lebesgue measure?

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