Sorority recruit questions
by: Elizabeth BathoryI am graduating from Rosemount high school mtl and have friends that joined sororities in BC. what are the things pnms get dropped for before or during recruitment? i’m not asking bc i want to “change my personality” or whatever bc i saw that accusation on another post, that said all AGDs think the same and if they don't believe the same idea they either get bullied out or change there mind to fit in. Just curious for recruitment
Commentby: Alpha Zeta Psi SecretsMay 21, 2020 2:03:33 PM
Now for f ∈ Lp, p ̸= ∞, we can truncate f in the domain and range to obtain bounded functions with compact support, fM → f . Since f −fM → 0 pointwise and |f −fM|p ≤ |f|p, dominated convergence shows ∥f −fM∥p → 0. Finally we can find step, continuous or smooth functions gn → FM pointwise, and bounded in the same way. Then |gn −FM |p → 0 by bounded convergence, so such functions are dense.
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by: Zeta Pres DR BonnerMay 21, 2020 2:04:49 PM
Lp as a completion. Given say V = C0∞(R) with the L2-norm, it is exceedingly natural to form the metric completion V of V and obtain a Banach space. But what are the elements of this space? The virtue of measurable functions is that they do suffice to represent all elements of V .
It is this completeness that makes measurable functions as important as real numbers.
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by: Real ANALysis SlayersMay 21, 2020 2:07:04 PM
Duality. Given a Banach space X, we let X∗ denote the dual space of bounded linear functionals φ : X → R, with the norm
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by: Cancer LancerMay 21, 2020 2:02:42 PM
Proof. First we treat f ∈ L . Then f is bounded, so it is a limit of simple functions in the usual way (cut the range into finitely many small intervals and round f down so it takes values in the endpoints of these intervals).
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