Sentence examples for measurable subset of from inspiring English sources

Then there is a constant (C>0) depending only on p and on the weight W such that if (f inmathbb{GT}_{n}) ((1 leq n inmathbb{R}^)) with each (r_{j} geq2) in its representation (1.1) and E is a measurable subset of ([0, 2pi]) of measure at most (lambdain 0, 1]), then int_{[0, 2pi]} f^{p} W leq C^{1+nlambda} int_{[0, 2pi]setminus E} f^{p} W. (4.1).

Let be a Lebesgue measurable subset of and denote the Lebesgue measure of.

For simplicity, we assume that Ω is a bounded Lebesgue measurable subset of ({mathbf{R}}^{n}) with Lebesgue measure equal to 1 and origin lies in Ω.

Let Ω be a measurable subset of a compact group G of positive Haar measure.

Let be a measurable subset of.

Let E is any measurable subset of Ω.

Norms in Hilbert spaces are denoted by ∥ ⋅ ∥ H α, ∥ ⋅ ∥ 0 is used to denote the supremum norm of real functions, i.e., for f : R → R we have ∥ f ∥ 0 = sup z ∈ R | f ( z ) |, and | ⋅ | denotes either the absolute value for scalars or the Lebesgue measure for measurable subsets of Euclidean space.

Banach showed in 1923 that Lebesgue measure is not the unique rotation invariant finitely additive probability measure on the measurable subsets of S1.

We also establish the extensions of this inequality to maps with values in measurable subsets of a measure space and to maps with values in subspaces of a linear space.

Specifically, suppose μ a measure on ( T, B ( T ) ) ( B ( T ) is the σ-algebra of Lebesgue measurable subsets of T) which is equivalent to the Lebesgue measure and verifies ∫ T r x ( t, t ) d μ ( t ) < ∞ (9).

Let, let be the Lebesgue measurable subsets of, and let be the Lebesgue measure on.