... set B is h'-upper measurable and P(BB) can be represented as the Choquet integral with respect to h". Definition 9.5. Let (Q ... empty set Q, let fo(Q) be the class of all subsets of Q. An outer measure is a function u": £2(Q) → [0, +2] such ...
... empty trace is denoted by €. In some cases the transition system will not be distinguished from its initial state (or the state on which it is). Furthermore we will use s + (or s +) to denote Hs' : s + s' (or Hs' : s # 8'). Definition 2 ...
Richard Hubert Bruck. Let P be any non-empty set, H be any group, and define products in P X H X P as follows: (p, h, q) (q, h', r) = (p, h h', r) (5.1) for all p, q, r in P, h, h' in H, and (p, h, q) (r,h', s) is not defined if q = r ...
Jan Gullberg. Sets of Numbers Notation Reads Ø N N * Z * " The empty set " Definition Ø = { } " The set of natural ... Q " The set of rational numbers " Q Z Z N N N N GORHERO Q + " The set of positive rational numbers " N = { 0 , N * ( 1 ...
... empty. Then, for any class A, the algebra P/Q(A) belongs to ISPIS (A). For let Q be the set of all congruence ... definition depends only on the cardinality of X but not on the actual set X nor on the way in which the particular algebra ...
... define a coalition-uniform set of strategies FA = {fa : a e A} for coalition A = {a 1, ..., ar) as follows: for every a = a, e A and any q' e Q, f, (q') = cy, where (c1, ..., cr) = foa (q). For q' = q 1 and a e A, fa (q') = empty. From ...
... Q does not contain an add_element message. This proof goal is reduced by unfolding the definition of the persistently_non_empty predicate, choosing to show that the set process will signal that it is empty when queried, and performing a ...
... set of labels , and l : T → A is a labelling . A marking is a function M : P → IN which associates to each place a ... Definition 6. For a set Q of places of a Petri net , we define NORM ( Q ) ( M ) to be the length of a shortest sequence ...
No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
... defined function. Definition 7 (State Monoid). Let C be a set, and for each c e C, let Q. be a non-empty set. Define the monoid SM (C, Qcec) = (C → Qcec, ...,0) where: – fl. fo = fi U fo, if dom(fi) Odom (f2) = 0 " * undefined ...