Many different invariant measures can be associated to any one evolution rule.

In fact, the invariant measure of this group is hyperbolic angle.

Proper lengths provide an invariant measure, whose value is the same for all observers.

There is no translation invariant measure on two-dimensional local fields.

The invariant measure for x is the uniform density over the unit interval.

Ergodic theory is the study of invariant measures in dynamical systems.

Ergodic theory - the study of dynamical systems with an invariant measure, and related problems.

For many dissipative chaotic systems the choice of invariant measure is technically more challenging.

The invariant measure in the first example is unique up to trivial renormalization with a constant factor.

Therefore the concept of quasi-invariant measure is the same as invariant measure class.

In 1951 he was awarded his habilitation for a dissertation on dynamical systems with invariant measure.

The special case of invariant measure for second countable locally compact groups had been shown by Haar in 1933.

Invariant measures on locally compact groups have long been used in statistical theory, particularly in multivariate analysis.

In mathematics, an invariant measure is a measure that is preserved by some function.

The invariant measure function is actually the prior density function encoding 'lack of relevant information'.

Specifically, the invariant measure is .

The weight function is chosen to produce a scale equivariant and rotation invariant measure that doesn't go to zero for dependent variables.

As a locally compact abelian group, the adeles have a nontrivial translation invariant measure.

Alexander Lubotzky, Discrete groups, expanding graphs and invariant measures.

Stochastic climate dynamics: Random attractors and time-dependent invariant measures.

The ground state may or may not commute with the generators of the symmetry; if commutes, it is said to be an invariant measure.

Existence of finite invariant measures for Markov processes, Proc.

Even in these cases, the number of ergodic invariant measures of is finite, and is at most .

Suppose that we have a set of discrete points , such that in the limit their density approaches a function called the invariant measure.

Then one-dimensional Lebesgue measure λ is an invariant measure for T.