Question

Suppose $A_i \in \mathcal{M}$, $A_1 \supset A_2 \supset \cdots \supset A_n \supset A_{n+1} \supset \cdots$ (a) If $m(A_1) < \infty$, show that $m\left(\bigcap_{n=1}^{\infty} A_n\right) = \lim_{n\to\infty} m(A_n)$. (b) Show by example that if $m(A_1) = \infty$, the above conclusion may be wrong.

          Suppose $A_i \in \mathcal{M}$, $A_1 \supset A_2 \supset \cdots \supset A_n \supset A_{n+1} \supset \cdots$
(a) If $m(A_1) < \infty$, show that
$m\left(\bigcap_{n=1}^{\infty} A_n\right) = \lim_{n\to\infty} m(A_n)$.
(b) Show by example that if $m(A_1) = \infty$, the above conclusion may be wrong.

Suppose Ai ∈ℳ, A1 ⊃ A2 ⊃⋯⊃ An ⊃ An+1⊃⋯
(a) If m(A1) < ∞, show that
m(⋂n=1^∞ An) = limn→∞ m(An).
(b) Show by example that if m(A1) = ∞, the above conclusion may be wrong.

Added by David S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Aman Gupta

04/30/2021

Step 1

Step 1: Given that m(A) < ∞, we want to show that lim n->∞ m(An) = 0. Show more…

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Suppose Ai E M,A1 J A2 ... An An+1 : (a) If m(A)< oo,show that 8 m n An n=1 lim m(An). n-> (b) Show by example that if m(A) = o, the above conclusion may be wrong