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By Rudolf Steiner

ISBN-10: 1855841940

ISBN-13: 9781855841949

Together with his philosophical and clinical education, Steiner introduced a brand new systematic self-discipline to the sphere of non secular learn, taking into consideration totally unsleeping equipment and complete effects. A typical seer, he cultivated his religious imaginative and prescient to a excessive measure, permitting him to talk with authority on formerly veiled mysteries. Samples of his paintings are to be present in this booklet of edited texts, which gathers excerpts from his many talks and writings on a variety of issues and have editorial introductions, observation, and notes. Chapters: The Continent of Atlantis The relocating Continents The historical past of Atlantis The Earliest Civilizations The Beginnings of notion Etheric know-how: Atlantean Magical Powers Twilight of the Magicians The Divine Messengers Atlantean mystery wisdom: Its Betrayal and next destiny The Origins of the Mysteries Atlantis and non secular Evolution

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Definition 2. A system of sets ~ is called a semiring if it contains the empty set, is closed with respect to the operation of intersection, and has the property that if A and A1 s;;;; A belong to ~. n then A can be represented in the form A = U Ak, where the Ak k=l are pairwise non-intersecting sets of given set A1. ~. the first of which is the In the following pages we shall call each system of non-intersecting sets A1, A2, · · ·, An, the union of which is the given set A, a finite decomposition of the set A.

L is called countably additive (or u-additive), if, for any sets A, A1, ···,An, ···,belonging to its domain of definition Sp. and satisfying the conditions Definition 1. L(An) n-1 holds. The plane Lebesgue measure which we constructed in §1 is u-additive (Theorem 9 ). An example of a u-additive measure of a completely different kind can be constructed in the following way. Let 36 I. MEASURE THEORY be an arbitrary countable set, and let the numbers Pn > 0 be such that L Pn = 1. The domain Sp. consists of all subsets of the set X.

The system 9R of Lebesg·ue measurable sets is a Borel algebra with unit E. Proof. Since 0n An = E"'Un (E""An), and since the complement of' a measurable set is measurable, it suffices to show the following. If A1, A 2, ···,An, · · · belong to 9R, then A = U An also belongs to 9)1. The proof of this statement n given in Theorem 8, §1, for plane sets, is literally preserved also in the general case. 44 I. L is a u-additive measure, defined on a B-algebra, A1 ::2 A 2 ::2 • • · ;;;;? L(An). The proof given in §1 for a plane measure (Theorem 10) can be carried over to the general case.

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Atlantis: The Fate of a Lost Land and Its Secret Knowledge (Esoteric) by Rudolf Steiner


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