1. Prove that, if F is Borel field in N, then(i) o E F(ii) whenever A1,A2, ... E F, then also N1 4; € F.(iii) whenever A1, A2, ... , An E F, then also U, A¡ € F and(iv) whenever A, B E F, then also A – BE F.

Definition of Borel field: Let Ω be a space. Let ℱ be a collection of subsets of Ω. Then ℱ is said…

1. Prove that, if F is Borel field in 2, then (i) ø E F (ii) whenever A,,A2, ... E F, then also N1 A E F. (iii) whenever A1, A2, .. , An E F, then also U, A € F and (iv) whenever A, B E F, then also A – BE F.

1. Prove that, if F is Borel field in 2, then (i) ø E F (ii) whenever A,,A2, ... E F, then also N1 A E F. (iii) whenever A1, A2, .. , An E F, then also U, A € F and (iv) whenever A, B E F, then also A – BE F.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1. Prove that, if F is Borel field in N, then
(i) o E F
(ii) whenever A1,A2, ... E F, then also N1 4; € F.
(iii) whenever A1, A2, ... , An E F, then also U, A¡ € F and
(iv) whenever A, B E F, then also A – BE F.

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