Daniel Bonilla Jaramillo Haase

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measure-theory

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6

What my did my Set Theory teacher mean when he said that there isn't an axiomatic system based on modal logic that serves as a foundation for math?

Jan 21, 2020

3

Variables vs. Constants, how are they defined in ZFC, and how they differ?

Dec 16, 2020

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Prove that for every $\varepsilon>0$ there is a measurable $E$, with $\mu(E)<\infty$, such that $\int_\Omega{f}d\mu \leq\int_E{f}d\mu+\varepsilon$

Nov 7

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Let $f:[0,1]\mapsto [0,\infty]$ be a bounded, measurable function, prove that $\int_{[0,1]} f\text { }dm=\inf\int_{[0,1]} \phi\text { }dm$

Nov 17

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Proof verification: If $f:[0,1]^2\mapsto\mathbb{R}$ is continuous, then $f$ is not injective

May 21, 2022

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measure-theory

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discrete-mathematics

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+20

Let $f:[0,1]\mapsto [0,\infty]$ be a bounded, measurable function, prove that $\int_{[0,1]} f\text { }dm=\inf\int_{[0,1]} \phi\text { }dm$

+20

Prove that for every $\varepsilon>0$ there is a measurable $E$, with $\mu(E)<\infty$, such that $\int_\Omega{f}d\mu \leq\int_E{f}d\mu+\varepsilon$

+10

Caratheodory's Theorem: finite measure implies unique and finite extension

+10

Carathéodory's theorem and $\sigma$-finite measures

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