doesn't exist a closed subset $F$ of $[0,1]$ such that $F\subset\mathbb{R}\setminus\mathbb{Q}$, and $|F|=1$ Axler Measure, Integration & Real Analysis

score 49 · Answer 12 · 2023-02-26 07:13:30

49

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Prove that $λ^{∗}_{1} (A) + λ^{∗}_{1} (B) ≤ λ^{∗}_{1}(A + B)$

Published on 26 Feb 2023 - 7:13

score 261 · Answer 13 · 2023-03-04 16:40:14

261

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Do we need intervals to define the Lebesgue measure?

Published on 04 Mar 2023 - 16:40

score 52 · Answer 14 · 2023-04-09 09:55:20

Are all subsets of $X$ $m$-measurable for $m(A):=\inf\{\sum_{i=1}^\infty\text{diam}(C_i):A\subset\bigcup_{i=1}^\infty C_i,C_i\subset X\}$?

score 60 · Answer 15 · 2026-03-25 17:19:14

60

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A detail on the Polar Coordinate Theorem proof

Published on 25 Mar 2026 - 17:19

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doesn't exist a closed subset $F$ of $[0,1]$ such that $F\subset\mathbb{R}\setminus\mathbb{Q}$, and $|F|=1$ Axler Measure, Integration & Real Analysis

Prove that $λ^{∗}_{1} (A) + λ^{∗}_{1} (B) ≤ λ^{∗}_{1}(A + B)$

Do we need intervals to define the Lebesgue measure?

Are all subsets of $X$ $m$-measurable for $m(A):=\inf\{\sum_{i=1}^\infty\text{diam}(C_i):A\subset\bigcup_{i=1}^\infty C_i,C_i\subset X\}$?

A detail on the Polar Coordinate Theorem proof

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