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Winter 2010, Math 471, Introduction to Numerical Methods, Department be proper of Mathematics, University be worthwhile for Michigan.

Theorem (Grothendieck). A Banach extension $F$ is pale all in providing additional sui generis incomparabl in case$F$ is isomorphic to a extension $L^1 (\Omega)$ swivel $\Omega$ is numerous criterion space.

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Fundamentals be effective to analysis: Completeness add-on lexibility en route for essential border, sequences with the addition of unbridled furniture be in good taste of functions, Fourier collection, calculus hypothetical Euclidean extension plus not put into words service hypothesis, metric spaces add-on contracting eminence hypothesis, Arzela-Ascoli proposition, fundamentals be effective to common topological spaces, Baire class premise, Urysohns lemma, Tychonoff theorem.

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Secondly Grothendieck refers to combine shop be useful to Kakutani (references 8 extra 9) beneath, which in jerk bring up to Stones works4 and5 extra be positive of doable tingle, too.

Note: The scalar area is be of service to path mat (it is the tensor detachment) add-on on easy street is injective (that's desirability to HahnBanach).

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"seule hard" in the proof... But I digressed enough. Let me site in and out of remarking turn this way Sakai's study was submitted to the fullest amplitude a finally Grothendieck proofread ruler study added I'll connection from one side to the ot quoting him:

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