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1. Consider a function : DR where DCR is measurable. Show that the following are equivalent: (i) is measurable. (ii) -¹(O) is measurable for every open set OCR. (iii) ¹(B) is measurable for every Borel set BCR.

1. Consider a function : DR where DCR is measurable. Show that the following are equivalent: (i) is measurable. (ii) -¹(O) is measurable for every open set OCR. (iii) ¹(B) is measurable for every Borel set BCR.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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1. Consider a function : D→ R where DCR is measurable. Show that the following are equivalent: (i) is measurable. (ii) -¹(O) is measurable for every open set OCR. (iii) ¹(B) is measurable for every Borel set BC R.
Transcribed Image Text:1. Consider a function : D→ R where DCR is measurable. Show that the following are equivalent: (i) is measurable. (ii) -¹(O) is measurable for every open set OCR. (iii) ¹(B) is measurable for every Borel set BC R.
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