Home > Analysis, Olympiad, Problem Solving > Average on Circles is constant

Average on Circles is constant


Prove that if the function f:\mathbb{R}^2 \to [0,1] is continuous and its average on every circle of radius 1 equals the function value at the center of the circle, then f is constant.
Miklos Schweitzer 1983

Advertisements
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: