This is characteristic of Minkowski functionals defined via " nice " sets.
2.
By definition of the Minkowski functional " p K ", one has
3.
Other sublinear functions can be useful as well, especially Minkowski functionals of convex sets.
4.
There is a one-to-one correspondence between seminorms and the Minkowski functional given by such sets.
5.
For an absorbing set such that if is in, then is in whenever, define the Minkowski functional of to be
6.
For one thing, while it's obvious to me that given some set we can induce a Minkowski functional by definition, it's not obvious to me that conversely by defining a seminorm p _ j, we induce some neighbourhood for which it is the Minkowski functional.
7.
For one thing, while it's obvious to me that given some set we can induce a Minkowski functional by definition, it's not obvious to me that conversely by defining a seminorm p _ j, we induce some neighbourhood for which it is the Minkowski functional.
8.
Are we defining seminorms p _ j ( with the factor of j at the start to ensure they're increasing ), and then saying'these must be the Minkowski functionals for "'some "'decreasing base of neighbourhoods of 0', and then using the fact that convergence under the suggested metric occurs only if convergence occurs for each p _ j?
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