Add spaces: ThefilmshowsInuitlifeasitisrightnow.Nocompromiseorcosmetics,ApVerheggensaystogreenlandtoday.

Answer: The film shows Inuit life as it is right now. No compromise or cosmetics, Ap Verheggen says to greenland today.

Add spaces: Thepurityandfreshnessareamazing!

Answer: The purity and freshness are amazing!

Add spaces: ...thatthebasisfortheapplicabilityoftheresultsofthemathematicaltheoryofprobabilitytoreal'randomphenomena'mustdependonsomeformofthefrequencyconceptofprobability,theunavoidablenatureofwhichhasbeenestablishedbyvonMisesinaspiritedmanner.

Answer:
... that the basis for the applicability of the results of the mathematical theory of probability to real 'random phenomena' must depend on some form of the frequency concept of probability, the unavoidable nature of which has been established by von Mises in a spirited manner.