Set-Valued Integrals
Set-Valued Integrals
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In our eReader you can find the full English version of the book. Read Set-Valued Integrals Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Set-Valued Integrals
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□ E E E Proof. Since \x has finite total variation, both u. and + 2 are Sv-integrable over any E in E by Theorem 2. Thus given any E in E, u = u + i\x is SA-integrable over E by Theorem 1.5. So / \x(da) = / (u . + iu )(da) = / p. (da) + i / n 2 (da) E E l l E l E The next theorem shows that in certain cases the SA-integral may be represented as a double Moore-Smith limit. In this theorem X is a ** ** normed linear space with second dual X . We regard X £ X 4. Theorem. Let ^:E -*■ X be finitely ...additive and s-bounded. If \i is SA-integrable over E e E, then f u(da) = lira, lim E u(E n E ) 1 ^ v J A n n E n Note. In Theorem 4, the conclusion gives us J ^t(da) e X, E even though it may happen that for a fixed A, 46 A ** v lim Eu(E n E ) e X \ X.
it ^ v n ** Proof. Considering \x as having range in the Banach space X , the 8- boundedness of |i implies (1) S E (A) = lim^ E^(E n E^) it exists in X** whenever A = (E ) is a disjoint sequence of sets in E (see [9])- The SA-integrability of \x over E implies there is an I(^,E) in X such that for any e > there is a A so that A > A £ implies there is a it with the property I(u,E) - Eu(E n E )|
What to read after Set-Valued Integrals?
You can find similar books in the "Read Also" column, or choose other free books by Sousa, Michael Joseph to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
□ E E E Proof. Since \x has finite total variation, both u. and + 2 are Sv-integrable over any E in E by Theorem 2. Thus given any E in E, u = u + i\x is SA-integrable over E by Theorem 1.5. So / \x(da) = / (u . + iu )(da) = / p. (da) + i / n 2 (da) E E l l E l E The next theorem shows that in certain cases the SA-integral may be represented as a double Moore-Smith limit. In this theorem X is a ** ** normed linear space with second dual X . We regard X £ X 4. Theorem. Let ^:E -*■ X be finitely ...additive and s-bounded. If \i is SA-integrable over E e E, then f u(da) = lira, lim E u(E n E ) 1 ^ v J A n n E n Note. In Theorem 4, the conclusion gives us J ^t(da) e X, E even though it may happen that for a fixed A, 46 A ** v lim Eu(E n E ) e X \ X.
it ^ v n ** Proof. Considering \x as having range in the Banach space X , the 8- boundedness of |i implies (1) S E (A) = lim^ E^(E n E^) it exists in X** whenever A = (E ) is a disjoint sequence of sets in E (see [9])- The SA-integrability of \x over E implies there is an I(^,E) in X such that for any e > there is a A so that A > A £ implies there is a it with the property I(u,E) - Eu(E n E )|
What to read after Set-Valued Integrals?
You can find similar books in the "Read Also" column, or choose other free books by Sousa, Michael Joseph to read onlineMoreLess
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