Let {fx: λE A} be a collection of µ-integrable func-tions on (N, F,μ).(i) If A is finite, then {fx : λ € A} is UI.(ii) If K = sup{ƒ|ƒx|¹+ dµ : λ € A} <∞o for some e > 0, then {fx : λ €A} is UI.(iii) If |fx| ≤g a.e. (μ) and fgdu

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Let {fx: λ € A} be a c F,μ). finite, then {f: A E A} is UI. sup{f|fx|¹+duAE A} <∞oj JI.

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

Section6.2: Applications Of Extrema

Problem 1YT: Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.

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Question

Let {fx: λE A} be a collection of µ-integrable func-
tions on (N, F,μ).
(i) If A is finite, then {fx : λ € A} is UI.
(ii) If K = sup{ƒ|ƒx|¹+ dµ : λ € A} <∞o for some e > 0, then {fx : λ €
A} is UI.
(iii) If |fx| ≤g a.e. (μ) and fgdu <oo, then {fx : AE A} is UI.
(iv) If {fx : λ € A} and {gy : 7 € I} are UI, then so is {fx +gy : λ €
Λ, γ ε Γ}.
(v) If {fx : λ € A} is UI and µ(N) < ∞o, then
sup
λελ
/ |fx|du <∞o.

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