O'Reilly logo

Stochastic Finance, 4th Edition by Alexander Schied, Hans Föllmer

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

A.6 Spaces of measures

Let S be a topological space. S is called metrizable if there exists a metric d on S which generates the topology of S. That is, the open d-balls

Bε(x) := {y S | d(x, y) < ε}, x S, ε > 0,

form a base for the topology of S in the sense that a set U S is open if and only if it can be written as a union of such d-balls. A convenient feature of metrizable spaces is that their topological properties can be characterized via convergent sequences. For instance, a subset A of the metrizable space S is closed if and only if for every convergent sequence in A its limit point is also contained in A. Moreover, a function f : S is continuous at y S if and only if f (yn) converges to f (y) for every sequence (yn) converging ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required