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Sn bu aj. The space of sequences has a natural vector space structure. The pnorm can be extended to vectors that have an infinite number of components (), which yields the space ℓ pThis contains as special cases ℓ 1, the space of sequences whose series is absolutely convergent,;. ` _ m h I æ w » É U F î Z Ö U 9 ` X o 1 q Q C 4 O w \ q ß Q h 0 p ( b s â ^ Q t h Ï o ª » p Ç Z p V Ý ï Â Æ ï.
` w ¤ p ò a q { Â å µ U K y z S ð U r > b \ q l o î x h X ^ K b. 5 {B∩ AB∈ A} Assume σ(A) = F Show that σ(A∩ A) = F ∩ A, relative to A Definition 12 Let Ω = R and B 0 the field of right–semiclosed intervals Then σ(B 0) = B is called the Borel σ–algebra of R Problem 12 Prove that every open set in R is the countable union of right. è Í Index Å t ù d o ± » Ó ~ § å ¬ R p V < h T s å ï ¿ Ó f w w ;.
` w ¤ w S ð t S Q ` b { µ Ð É i T ® p V ¯ \ q M M 5 Ô w ;. ℓ 2, the space of squaresummable sequences, which is a Hilbert space, and;. ℓ ∞, the space of bounded sequences;.
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