Second Order Differential Operators on the Configuration Spaces

Γ = { γ ⊂ R ∣∣ |γΛ| < +∞ for any compact Λ ⊂ Rd}, where | · | means the cardinality of a set and γΛ = γ ∩ Λ. Let us define the σ-algebra B (Γ) as the minimal σ-algebra such that all mappings Γ γ −→ |γΛ| are B(Γ)-measurable for any Λ ∈ Bc(R), where Bc(R) is the family of all Borel subsets of Rd with compact closure. The space Γ can be naturally embedded into the space M(Rd) of all measures on Rd in the following way