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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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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