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As in the case of an L2-space, an -function is really an equivalence class of functions which agree almost everywhere.

It is possible for a sequence of functions to converge in but not in for some other , e.g., converges in but not .

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The -space on , and in most other cases, is the completion of the continuous functions with compact support using the norm.However, if a sequence converges in and in , then its limit must be the same in both spaces.For 1" /, the dual vector space to is given by integrating against functions in , where .(born 7 July 1940), known professionally as Ringo Starr, is an English drummer, singer, songwriter and actor who gained worldwide fame as the drummer for the Beatles.He occasionally sang lead vocals, usually for one song on an album, including "With a Little Help from My Friends", "Yellow Submarine" and their cover of "Act Naturally".Then define a "norm" on this space as is usual in the non-negative case: $\| f\| = (\int|f|^dx)^$.If $f$ is equal to zero on a set of positive measure it makes sense to interpret the integral as having an infinite value, which would make the "norm" equal zero.New Dating will introduce you to Russian brides seeking their dream, romance, love and marriage.Our international dating service is for singles seeking for friendship, romance, dating, long-term relations and international marriage.Let $p$ be a negative real number and $X$ a measure space.Define $L^p(X)$ to be the vector space of all measurable functions $X \to \mathbb$.