Question

Assume that μ is a countably additive function defined on a ring $\large\rm{ R,A, A_{n} \in R}$ that $\large\rm{ A_{1} \subseteq A_{2} \subseteq \dots,}$ and $\large\rm{ A = \bigcup\limits_{n=1}^{\infty} A_{n}}$

Prove that $\large\rm{ \lim\limits_{n \to \infty} \mu (A_{n} ) = \mu (A)}$​

Answer 1

Answer:

Assume that μ is a countably additive function defined on a ring $\large\rm{ R,A, A_{n} \in R}$ that $\large\rm{ A_{1} \subseteq A_{2} \subseteq \dots,}$ and $\large\rm{ A = \bigcup\limits_{n=1}^{\infty} A_{n}}$

Prove that $\large\rm{ \lim\limits_{n \to \infty} \mu (A_{n} ) = \mu (A)}$

Answer 2

Answer:

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Step-by-step explanation:

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