For constant-exponent cases, Lazer and Mckenna in [5] discussed the case when (p=2) and f is a positive regular function in Ω̅.
where G : [ 0, 1 ] × R d → P ( R d ) is a closed convex-valued multifunction and μ is a positive regular Borel measure.
In this paper, we initiate the study of a class Dmp(H) of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space H, where m⩾2, n⩾2, and p is a positive regular polynomial in n noncommutative indeterminates.
For smooth (u) we then have begin{aligned} (dd^cu ^n=dd^cuwedge dots wedge dd^cu =4^nn!det (partial ^2u/partial z_jpartial bar{z}_k),dlambda end{aligned}and one would like to define ((dd^cu ^n) as a positive regular measure for arbitrary plurisubharmonic (u).
In the following, if T is a Polish space (that is, a separable complete metric space) endowed with a positive regular Borel measure μ, we shall denote by ({mathcal{T}}_{mu}) the completion of the σ-algebra ({mathcal{B}}(T)) with respect to the measure μ.
Let T, X be two Polish spaces, and let μ be a finite positive regular Borel measure on T. Let (Wsubseteq X) be a Souslin set, (f Ttimes Wto{mathbf{R}}) a given function, (Esubseteq W) another set.
On a positive note, regular exercise, coupled with a reasonable quota of oily fish, extra virgin olive oil and raw garlic in the diet, can help to boost HDL levels.
They derived many results on the existence and the multiplicity of positive (regular) solutions by applying topological degree and variational approach, respectively.
Let (mu, psi_{1},ldots,psi_{k}) be positive regular Borel measures over (T,X_{1},X_{2},ldots, X_{k}), respectively, with μ finite and (psi_{1},ldots,psi_{k}) σ-finite.
Let (pin{mathbf{N}}), with (pge2), and let (Y_{1},Y_{2},ldots, Y_{p}) be Polish spaces, endowed with σ-finite positive regular Borel measures (mu_{1},ldots},mu_{p}mu_{p}), respectively.
Let μ, (psi_{1},ldots,psi_{k}) be positive regular Borel measures over T, (X_{1},X_{2},ldots, X_{k}), respectively, with μ finite and (psi_{1},ldots,psi_{k}) σ-finite.
