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15. If S1 and S2 are two semialgebras of subsets of 2, show that the class S1S2 := {A1A2 : A1 € S1, A2 € S2} is again a semialgebra of subsets of 2. The field (o-field) generated by S1S2 is identical with that generated by S1 U S2.

15. If S1 and S2 are two semialgebras of subsets of 2, show that the class S1S2 := {A1A2 : A1 € S1, A2 € S2} is again a semialgebra of subsets of 2. The field (o-field) generated by S1S2 is identical with that generated by S1 U S2.

Advanced Engineering Mathematics
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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15. If S1 and S2 are two semialgebras of subsets of S, show that the class S1S2 := {A1A2 : A1 e S1, A2 e S2} is again a semialgebra of subsets of N. The field (o-field) generated by S1S2 is identical with that generated by Si U S2.
Transcribed Image Text:15. If S1 and S2 are two semialgebras of subsets of S, show that the class S1S2 := {A1A2 : A1 e S1, A2 e S2} is again a semialgebra of subsets of N. The field (o-field) generated by S1S2 is identical with that generated by Si U S2.
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