3 1 3 distributions examples and rules of calculus 3 1 distributions the space c is often denoted d in the literature the distribu 0 tions are simply the elements ...
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...Distributions examples and rules of calculus the space c is often denoted d in literature distribu tions are simply elements dual denition a distribution on continuous linear functional vector when we denote value by or h i tradition here to take rather than conjugate func tionals but it easy change functionals if needed for only see theorem how continuity checked itself provided with weak topology e topol ogy dened system seminorms p u hu where runs through use b noting that family separating since means some let us consider f l loc then map z x dx have every kj cf sup so satised n kfk one can fact j identify view following lemma r all proof v as y from conclude values follows variants sometimes called fundamental variations du bois reymond s implies gives test functions function equal an element injective may write will now be identied usual representative lp these also naturally jected remark mention radon measures t compact support topological measure theory shown m complex such wa...