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The weaker notion that markets, particularly financial markets, usually work pretty well, and it's very hard to beat them by investing against them, that I think is still very powerful.
It is weaker notion of the robustly transitivity.
There is a weaker notion of amenability introduced by D. Voiculescu.
In [11], Barreira and Valls discussed the much weaker notion of a nonuniform exponential dichotomy.
We introduce the notion of chain transitive set, which is a weaker notion of transitive set.
Being well-balanced up to second order is a weaker notion of well-balancing compared to being truly well-balanced.
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Remark 2.91 In recent works several authors claimed to introduce some weaker noncommuting notions and pretended to show, weak compatibility as a proper subclass of their weaker notions.
However, afterwards, we will use some weaker notions, namely we will need a notion that allows lower solutions to have 'angles'angles
We do such by proving that many known results regarding coarse and uniform embeddability remain valid for those weaker notions of embeddability.
There are some other weaker notions of stability in literature like substability [12, 17, 20, 21] which also hold when the queues satisfy stability.
It is important to remember that both IND-OCPA and IND-DCPA represent weaker notions of security based on IND-CPA.
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