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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_14” 2011/5/22 23:43 page 11 #11
L
p
-Spaces 14-11
14.5 GENERALIZATIONS
Most of the results that we have obtained for the space L
p
(R)(1 p <
) can be easily extended to the context of an abstract measure space
L
p
(µ) where (X , M, µ) is a measure space and
L
p
(µ) ={f : X C/f measurable with ||f ||
p
=
X
|f |
p
dµ
1/p
< ∞}
Indeed, each L
p
(µ) is a vector space and if we identify two functions
that are equal almost everywhere on X with respect to µ, then as before
we can regard L
p
(µ) as a metric space.
We shall now develop some preliminaries. (See also Section 10.4)
Definition 14.5.1 Let φ : D
R R be a function where D is an
interval. ...
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Publisher Resources

ISBN: 9781299447561Publisher Website