1. Let {f} be a sequence of integrable functions on E, i.e. fn L¹(E) Vn N. Suppose {fn} → f pointwise a.e. on E and fe L¹(E). Show that then iff-fal→0 E lim Selfml = Self. E E
1. Let {f} be a sequence of integrable functions on E, i.e. fn L¹(E) Vn N. Suppose {fn} → f pointwise a.e. on E and fe L¹(E). Show that then iff-fal→0 E lim Selfml = Self. E E
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Let {f} be a sequence of integrable functions on E, i.e. fn E L¹(E) Vn N. Suppose {f} → f
pointwise a.e. on E and f e L¹(E). Show that
if Self-ful → 0
If-
E
then Himal-V
E
lim
71-00
=
E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1e53067-1355-425c-b0db-fe5729e6444a%2F840f0c5f-46f9-42e1-8a21-416f953b8c46%2Fo2rzbbr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let {f} be a sequence of integrable functions on E, i.e. fn E L¹(E) Vn N. Suppose {f} → f
pointwise a.e. on E and f e L¹(E). Show that
if Self-ful → 0
If-
E
then Himal-V
E
lim
71-00
=
E
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