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Lebesgue measure In the content of the unit and in previous references we learned that if we denote by С a set of intervals of the form (-∞, a], (a,b], (b, ∞), then the set F-[Ünnec} i=1 = forms an algebra, however, not a sigma algebra, as we will see below. 1. Prove that (0,1) does not belong to F. Hint: Notice that in F the union of intervals is infinite. 2. Prove that: ∞ (0,1)= Ū(0,1 - 1] i=2 And from the above conclude that F cannot be a sigma algebra. Please be as clear as posible, legible and showing and explaining all the steps. Use definitions if necessary. Thank you a lot.

Lebesgue measure In the content of the unit and in previous references we learned that if we denote by С a set of intervals of the form (-∞, a], (a,b], (b, ∞), then the set F-[Ünnec} i=1 = forms an algebra, however, not a sigma algebra, as we will see below. 1. Prove that (0,1) does not belong to F. Hint: Notice that in F the union of intervals is infinite. 2. Prove that: ∞ (0,1)= Ū(0,1 - 1] i=2 And from the above conclude that F cannot be a sigma algebra. Please be as clear as posible, legible and showing and explaining all the steps. Use definitions if necessary. Thank you a lot.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
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Lebesgue measure In the content of the unit and in previous references we learned that if we denote by С a set of intervals of the form (-∞, a], (a,b], (b,∞), then the set F={Uwhec} C i=1 forms an algebra, however, not a sigma algebra, as we will see below. 1. Prove that (0,1) does not belong to F. Hint: Notice that in F the union of intervals is infinite. 2. Prove that: ∞ (0,1) = U(0,1 - 1] i=2 And from the above conclude that F cannot be a sigma algebra. Please be as clear as posible, legible and showing and explaining all the steps. Use definitions if necessary. Thank you a lot.
Transcribed Image Text:Lebesgue measure In the content of the unit and in previous references we learned that if we denote by С a set of intervals of the form (-∞, a], (a,b], (b,∞), then the set F={Uwhec} C i=1 forms an algebra, however, not a sigma algebra, as we will see below. 1. Prove that (0,1) does not belong to F. Hint: Notice that in F the union of intervals is infinite. 2. Prove that: ∞ (0,1) = U(0,1 - 1] i=2 And from the above conclude that F cannot be a sigma algebra. Please be as clear as posible, legible and showing and explaining all the steps. Use definitions if necessary. Thank you a lot.
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