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okay so welcome to this next video in the placed on functional analysis and in this video Im going to introduce you to the ELP spaces which are absolutely central to functional analysis now in a previous video weve seen the L infinity space the other infinity space is just a special case of an LP space so without further ado thats lets define what the LP space is so remember a metric space consists of a set along with a distance function which is mapping the Cartesian product of that set with itself onto a non-negative real number okay so well start with what is the set underlying the LP space well LP space if you remember from our infinity spaces L infinity spaces were they were there were steps which contained all sequences of real numbers such that such that the the sequence is bounded basically so that there is a supreme M of the sequence there is a that all the values of the sequence are within some interval and therefore you can define a supremum and then what we did is we
