Then, there exists a modification of the local time process (left (L^{X}left (t,xright),tgeq 0,,xin mathbb {R}right)) of X such that the map (t,x ↦L X (t,x) is continuous in t and càdlàg in x, P-a.s.s
There already exists a modification of GSEA that allows enrichment of pathways with bidirectional gene expression [ 39].
This constitutes the core of Spinoza's pantheism: God is everywhere, and everything that exists is a modification of God.
There exists a continuous modification (widetilde{X}(t)) of (X t)) which has the property that for every (varthetain 0,frac{beta}{alpha})) there is a positive random variable (h omega)) such that Pbiggl{ omega:sup_{0< |t-s|< h omega), 0leq s, t< infty} frac{widetilde {X} t,omega -widetilde{X}(s,omega -widetilde{X}heta}} leqfrac {2}{1-2^{-vartheta}}biggr} =1.
Then there exists a continuous modification X ˜ ( t ) of X ( t ), which has the property that for every γ ∈ ( 0, β α ), there is a positive random variable h ( w ) such that P { ω : sup 0 < | t − s | < h , 0 ≤ s, t < + ∞ | X ˜ ( t, ω ) − X ˜ ( s, ω ) | | t − s | γ ≤ 2 1 − 2 − γ } = 1.
Then there exists a continuous modification X ˜ ( t ) of X ( t ) which has the property that for every ϑ ∈ ( 0, α 2 / α 1 ), there is a positive random variable h such that P { ω : sup 0 < | t − s | < h , 0 ≤ s, t < ∞ | X ˜ ( t, ω ) − X ( t, ω ) | | t − s | ϑ ≤ 2 1 − 2 − ϑ } = 1.
Then there exists a continuous modification (tilde{x}(t)) of (x t)) which has the property that, for every (thetain 0,alpha_{2}/alpha_{1})), there is a positive random variable (h omega)) such that begin{aligned} P biggl{ omega: sup_{0< |t-s|< h omega),0< s,t< infty} frac{tilde {x} t,omega -x t,omega -x t-s|^{theta}}leq frac{2}{1-2^{-theta }} biggr} =1.
Following Descartes, Malebranche proclaims throughout his work that everything that exists is either a substance or a modification of a substance.
Supporting overlapping instances would need a modification of function ({ matches}) so as to select a single instance if there exist overlapping matching instances.
A modification of the plan is a one way conference.
A modification of pharmacotherapy.
