# Monthly Archive: May 2020

## Solution to Measure, Integration & Real Analysis

Chapter 1 Riemann Integration §1A Review: Riemann Integral §1B Riemann Integral Is Not Good Enough Chapter 2 Measures §2A Outer Measure on R §2B Measurable Spaces and Functions §2C Measures and Their Properties §2D...

## The quotient of a generating set is a generating set of the quotient

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.16 Let $G$ be a group and $N \leq G$ a normal subgroup. Show that if $G = \langle S \rangle$,...

## Q/Z is divisible

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.15 Prove that a quotient of a divisible abelian group by any proper subgroup is also divisible. Deduce that $\mathbb{Q}/\mathbb{Z}$ is...