Sentence examples for measures spaces from inspiring English sources

Recently, Hytönen [3] gave a new class of metric measures spaces ( X, d, μ ) (instead of ( R n, d, μ ) ), which are called non-homogeneous spaces, the measure μ satisfies the upper doubling condition (see definition 1.3).

The new class of metric measures spaces are sufficiently general to include in a natural way both the space of homogeneous type and a metric space with the mild volume growth condition.

We study tent spaces on general measure spaces.

Let and be -finite (positive) measure spaces and (1.10).

Hytönen [10] introduced the non-homogeneous metric measure spaces ((X,d,mu)), which contains the homogeneous spaces and non-doubling measure spaces.

When L φ ( A, X ) is a Bochner-Lebesgue space, which was obtained in [29] and [32, 33] on finite measure spaces and σ finite measure spaces, respectively.

In particular, we extend a recent compactness result of Edmunds and Opic for operators between Lp-spaces over finite measure spaces to σ-finite measure spaces.

The results are established for both the homogeneous spaces and the non-doubling measure spaces.

Our results include both the results for the homogeneous spaces and the non-doubling measure spaces.

For example, unlike the doubling measure spaces, we need delicate geometric observations (see (2.19) for example).

We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces.