[See Solution] Let \mathcalE be any collection of subsets of R. Show that there is always a smallest σ -algebra \mathcalA containing \mathcalE. [Hint:
Question: Let \(\mathcal{E}\) be any collection of subsets of \(\mathrm{R}\). Show that there is always a smallest \(\sigma\) -algebra \(\mathcal{A}\) containing \(\mathcal{E}\). [Hint: Show that the intersection of \(\sigma\) -algebras is again a \(\sigma\) -algebra.]
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![[Step-by-Step] The smallest α -algebra containing \mathcalE](/images/solutions/MC-solution-library-38404.jpg "[Step-by-Step] The smallest α -algebra containing \mathcalE")
[Step-by-Step] The smallest α -algebra containing \mathcalE
(All Steps) Show that \mathcalB is generated by each of the following:
(See Steps) Given any subset E of R and any h ∈ R, show that
![[Solution Library] Given δ>0, show that m^*(E)=](/images/solutions/MC-solution-library-38407.jpg "[Solution Library] Given δ>0, show that m^*(E)= ∈ f ∑_n=1^∞")
[Solution Library] Given δ>0, show that m^*(E)= ∈ f ∑_n=1^∞
(Step-by-Step) If E=∪_n=1^∞ I_n is a countable union of pairwise
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