(a) Show that it exists an interval I = [a, b], a, b = R₁ -∞ 0, so that (-E, E) CE-E \x, x< 2 → ((EnI)+)n(EnI) ‡ Ø

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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E € L(R) with 0 < X(E) < ∞ is a lebesgue-measure on
(R, B(R)).
We define
B,C C R, B – C := {x – y : x € B, y € C}.
|
X(I)
= ((EnI) +x) N (EnI)# Ø
2
Vx, |æ| <
(a) Show that it exists an interval ! = [a, 6], a, b E R, -∞ < a < b<∞so that
(b) Show that, it exists a € > 0, so that (-E, ɛ) C E – E
Transcribed Image Text:E € L(R) with 0 < X(E) < ∞ is a lebesgue-measure on (R, B(R)). We define B,C C R, B – C := {x – y : x € B, y € C}. | X(I) = ((EnI) +x) N (EnI)# Ø 2 Vx, |æ| < (a) Show that it exists an interval ! = [a, 6], a, b E R, -∞ < a < b<∞so that (b) Show that, it exists a € > 0, so that (-E, ɛ) C E – E
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