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## The union of a chain of ideals is an ideal

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.19 Solution: In Exercise 2.1.15, we saw that $S \subseteq R$ is an additive subgroup. To show…

## Union with a zero measure set does not alter the measure

Solution to Measure, Integration & Real Analysis by Axler Section 2A Exercise 2A1 Prove that if $A$ and $B$ are subsets of $\mathbf R$ and $|B|=0$, then $|A\cup B|=|A|$. Solution:…