Consider a nonnegative measurable funct that m({x € E : g(x) > M}) ≤ √ √ ² 9. M E Hint: Consider the simple function Mx consider two cases: M(A) < ∞o and m(A

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
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5. Consider a nonnegative measurable function g defined on E. If G is integrable over E, prove
that m({x € E : g(x) > M}) ≤ √ª·
Hint: Consider the simple function MXA, where A = {x € E : g(x) > M}. You need to
consider two cases: M(A) < ∞ and m(A) = +∞o.
(This is Chebychev's Inequality)
Transcribed Image Text:5. Consider a nonnegative measurable function g defined on E. If G is integrable over E, prove that m({x € E : g(x) > M}) ≤ √ª· Hint: Consider the simple function MXA, where A = {x € E : g(x) > M}. You need to consider two cases: M(A) < ∞ and m(A) = +∞o. (This is Chebychev's Inequality)
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