Cohn Measure Theory Solutions: ((full))

Step 2 – Necessity of finiteness. Take $X = \mathbb{R}$, $\mathcal{A} = \mathcal{B}(\mathbb{R})$ (Borel sets), $\mu = $ Lebesgue measure. Let $A = [0,\infty)$, $B = \mathbb{R}$. Then $A \subseteq B$, but $\mu(A) = \infty$. The right‑hand side $\mu(B) - \mu(A)$ is $\infty - \infty$, which is undefined in the extended real numbers. The left‑hand side $\mu(B\setminus A) = \mu((-\infty,0)) = \infty$. Thus the equality fails in the sense that the subtraction is not well‑defined. This shows $\mu(A) < \infty$ is necessary.

Folders and files. post the solutions of the problems of Donald Cohn's Measure Theory book here. Cohn-Measure-Theory-Solutions/README.md at main - GitHub

: For specific difficult problems (e.g., Exercises 1.3.9, 2.4.9, or 6.2.4), search Math Stack Exchange

Exercise 2.4.9 and 2.5.5 regarding Lebesgue integration and limits.

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