Linear Operators, Part 1 |
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Page 28
6 1 : D → X be a generalized sequence of elements in a metric space X. We call
f a generalized Cauchy sequence in X , if , for each a > 0 , there exists a d . € D ,
such that out ( p ) , f ( 9 ) ) < if p 2 do , I do . 5 LEMMA . If f is a generalized Cauchy
...
6 1 : D → X be a generalized sequence of elements in a metric space X. We call
f a generalized Cauchy sequence in X , if , for each a > 0 , there exists a d . € D ,
such that out ( p ) , f ( 9 ) ) < if p 2 do , I do . 5 LEMMA . If f is a generalized Cauchy
...
Page 362
Under the hypotheses of Exercise 37 , show that there exists f in C with an = $ * (
x ) n ( x ) dx if and only if the functions - commna dn ( x ) , m 2 1 , are uniformly
bounded and equicontinuous . 39 Let { an } , – 00 < n < too , be a bounded ...
Under the hypotheses of Exercise 37 , show that there exists f in C with an = $ * (
x ) n ( x ) dx if and only if the functions - commna dn ( x ) , m 2 1 , are uniformly
bounded and equicontinuous . 39 Let { an } , – 00 < n < too , be a bounded ...
Page 724
Show that m is potentially invariant if and only if the limit ñ ( e ) = limn - on - 1 = m
( q - ie ) exists for each e € £ , and that in is an element of ca ( S , E ) satisfying m (
q - le ) = m ( e ) . Hint . Consider the space of all u - continuous elements of ca ...
Show that m is potentially invariant if and only if the limit ñ ( e ) = limn - on - 1 = m
( q - ie ) exists for each e € £ , and that in is an element of ca ( S , E ) satisfying m (
q - le ) = m ( e ) . Hint . Consider the space of all u - continuous elements of ca ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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