In the next remark, we give a conditional equilibrium distribution of the subset of species with natural time scale exponents smaller than γ=1 and γ=2.
(The conditional is a condition.
We define S 1 = ∑ k = 1 K 1 A k C π k which by Remark 1.9 is indeed a conditional simplex.
Concerning the necessity aspect of mereological extensionality, i.e., the left-to-right conditional in the consequent of (27), it is perhaps enough to remark that the difficulty is not peculiar to extensional mereology.
When Mr. Gore's speech did allude to a few dark thoughts about the man he lost to four years ago, he framed the remarks in what might be called the optimistic conditional tense.
But it is implausible that the difficulties with the truth-functional conditional can be explained away in terms of what is an inappropriate conversational remark.
Remark 2 Our result is 'backward compatible' with previous results about the conditional oscillation of half-linear equations.
Remark 3.2 In Drapeau et al. [9] the concept of conditional compactness is introduced and it is shown that there is an equivalence between conditional compactness and conditional closed- and boundedness in ( L 0 ) d.
For an index set I and a collection S = ( S i ) i ∈ I of conditional simplexes, we denote ext ( S ) = σ ( ⋃ i ∈ I ext ( S i ) ). Remark 1.9 Let S j = conv ( X 1 j, …, X N j ), j ∈ N, be conditional simplexes of the same dimension N and ( A j ) j ∈ N a partition.
