# Download Maths en scène - Maths en Seine by Elisabeth Hébert (ed.) PDF

By Elisabeth Hébert (ed.)

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Pi und Co.: Kaleidoskop der Mathematik (German Edition)

Mathematik ist eine vielseitige und lebendige Wissenschaft. Von den großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen zu den aktuellen mathematischen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten.

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Then lim, Ιόχ = f(x) for all xeX. I PROOF Let x G #■ and e > 0. Then there are y0 G N and j G Χλ such that l/(*) - / ω ΐ < €/3, | j> - x | < e/3, and | / ( j ) - l, y \ < e/3 for ally > y 0 . Thus |/(x) - Ice I < |/(*) -f(y)\ + \fiy) - hy | + | /,Ο - x)\ < e for all j^j0. 11 Theorem (Bishop) Let X be a separable normed vector space and £/ Δ {/G#** | | /1 Δ s u p i ^ i | l(x)\ < 1}. Then there exists a norm I · \w (weak norm) on X* such that the relativizations to U of the corresponding metric topology (weak metric topology) and of the weak star topology of X* coincide, and lim, | / — /,,\w = 0 for /, /, G U if and only if lim,· IjX = Ix for each x e l I PROOF Let Χ^ Δ {jq , JC2 v··} be a dense subset of #" and n I Γ L Δ lim X 2"' | Tx5 |/(1 + | x,· |) n j=i for all Γ G X*.

And their diagonal subsequence (/,)3e

Ste/? 3 We now prove that for every A e Σ there exists A' C A with μ,(Λί') = \μ(Α). If M-4) = 0, then A' A A yields μ(Α') = \μ(Α). We therefore assume that μ{Α) > 0. , C%m) of C with 0 < MQ m ) < 1/ra.