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- #1

- Feb 5, 2012

- 1,621

Here's one of the questions I had when trying to solve a problem.

Let \(K\subset \mathbb{R}^{n}\) be a closed symmetric convex subset with non empty interior. Let \(\alpha>\beta\) where \(\alpha,\,\beta\in \mathbb{R}\). Then prove that,

\[\beta K\subset\alpha K\]

I have tried various things but didn't get a breakthrough. Any hint on how to solve this would be greatly appreciated.