𝗖𝗼𝗻𝗱𝗶𝘁𝗶𝗼𝗻𝗮𝗹 𝗲𝘅𝗽𝗲𝗰𝘁𝗮𝘁𝗶𝗼𝗻: 𝗮 𝗰𝗼𝗺𝗽𝗮𝗿𝗶𝘀𝗼𝗻 𝗯𝗲𝘁𝘄𝗲𝗲𝗻 𝘁𝗵𝗲 𝗮𝘅𝗶𝗼𝗺𝗮𝘁𝗶𝗰 𝗮𝗽𝗽𝗿𝗼𝗮𝗰𝗵 𝗮𝗻𝗱 𝘁𝗵𝗲 𝘀𝘂𝗯𝗷𝗲𝗰𝘁𝗶𝘃𝗲 𝗮𝗽𝗽𝗿𝗼𝗮𝗰𝗵

In the subjective approach conditional expectation cannot be defined by the Radon-Nikodym derivative.It occurs because one of the defining property of the Radon-Nikodym derivative, that is to be measurable with respect to the sigma-field of the conditioning events, contradicts a necessary condition for the coherence.

𝗣𝗿𝗼𝗳.𝘀𝘀𝗮 𝗦𝗲𝗿𝗲𝗻𝗮 𝗗𝗼𝗿𝗶𝗮
𝗗𝗼𝗰𝗲𝗻𝘁𝗲 𝗱𝗶 𝗖𝗮𝗹𝗰𝗼𝗹𝗼 𝗱𝗲𝗹𝗹𝗲 𝗣𝗿𝗼𝗯𝗮𝗯𝗶𝗹𝗶𝘁𝗮̀ 𝗲 𝗦𝘁𝗮𝘁𝗶𝘀𝘁𝗶𝗰𝗮 𝗠𝗮𝘁𝗲𝗺𝗮𝘁𝗶𝗰𝗮 - 𝗥𝗲𝘀𝗽𝗼𝗻𝘀𝗮𝗯𝗶𝗹𝗲 𝗱𝗲𝗹 𝗣𝗿𝗼𝗴𝗲𝘁𝘁𝗼 𝗨𝗱'𝗔 𝗦𝗰𝗶𝗲𝗻𝘇𝗮
𝗗𝗶𝗽𝗮𝗿𝘁𝗶𝗺𝗲𝗻𝘁𝗼 𝗱𝗶 𝗜𝗻𝗴𝗲𝗴𝗻𝗲𝗿𝗶𝗮 𝗲 𝗚𝗲𝗼𝗹𝗼𝗴𝗶𝗮 𝗨𝗱'𝗔

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