Sentence examples for measures μ typically from inspiring English sources

We show that such spectral pairs have a self-similarity which may be used to generate associated fractal measures μ (typically with Cantor set support).

The sequence of measures μ n converges weakly to μ.  .

That is, P consists of all positive Borel measures μ on Ω that satisfy μ = 1.

Moreover, it can be shown that the measure μ can be naturally and uniquely extended to the set of all measurable sets, where the measure defined has corresponding nice properties (so that, e.g., the measure of the complement of E is 1 − μ(E), if E ⊆ F then μ(E) ≤ μ(F), etc).

The measure μ is a probability measure if μ(M) = 1.

A measure μ on the locally compact abelian group G is "Lp-improving" if for some 1⩽p<r<∞, μ∗Lp(G ⊆Lr G).

In particular we prove that each measure μ of the class Mp is uniquely determined by its μ-capacity.

Let a countable amenable group G act freely and ergodically on a Lebesgue space (X, μ), preserving the measure μ.

An important feature of X is that it is endowed with a so-called measure μ.

For any f-invariant probability measure μ, we have μ ( Σ f ) = 1.

Then the invariant measure μ is called the Sinai-Ruelle-Bowen meaSRBe, or SRB measure, of f.