By S. M. Srivastava (auth.)

ISBN-10: 3642854737

ISBN-13: 9783642854736

ISBN-10: 3642854753

ISBN-13: 9783642854750

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**Extra info for A Course on Borel Sets**

**Example text**

In X. Define d(x,1/) = L 2n~1 min{dn(xn,1/n),1}. n Then d is a metric on X, which we shall call the product metric. Note that if (X, d) is a metric space and Y ~ X, then d resticted to Y (in fact to Y x Y) is itself a metric. Thus we can think of a subset of a metric space as a metric space itself and call it a subspace of X. Let (X, d) be a metric space, x EX, and r > O. We put B(x,r) = {y EX: d(x,1/) < r} and call it the open ball with center x and radius r. The set {y EX: d(x,1/) :'5 r} will be called the closed ball with center x and radius r.

Ylm' 'YeN" m We need to define a system of sets {C. : xEX, I E N Uniqueness) Let f,g : T --+ X satisfy (*). £) = g(u}. • Let T be a well-founded tree. £ E T. £ is terminal in T. The map PT is called the rank function of T. Finally, we define peT) = PT(e} and call it the rank of T. 4 p(T) = sup{PT(u·a) + 1: u·a E T}. lsi ifT= {sli: i < lsi}, s E N## A Course on Borel Sets by S. M. Srivastava (auth.)

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