O'Reilly logo

Convex Bodies: The Brunn–Minkowski Theory, Second Edition by Rolf Schneider

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

1

Basic convexity

1.1 Convex sets and combinations

A set image is convex if together with any two points x, y it contains the segment [x, y], thus if

image

Examples of convex sets are obvious; but observe also that B0(z, ρ) ∪ A is convex if A is an arbitrary subset of the boundary of the open ball B0(z, ρ). As immediate consequences of the definition we note that intersections of convex sets are convex, affine images and pre-images of convex sets are convex, and if A, B are convex, then A + B and λA are convex.

Remark 1.1.1 For and λ, μ > 0 one trivially ...

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